00-XX

总论

General

00-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

00-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

00Axx

一般的和各种特殊的课题

General and miscellaneous specific topics

00A05

普通数学

General mathematics

00A06

非数学家的数学(工程、社会科学等)

Mathematics for nonmathematicians (engineering, social sciences, etc.)

00A07

问题集

Problem books

00A08

趣味数学[参见97A20]

Recreational mathematics [See also 97A20]

00A09

数学普及

Popularization of mathematics

00A15

书目

Bibliographies

00A17

外国书评

External book reviews

00A20

辞典和其它一般参考书

Dictionaries and other general reference works

00A22

公式集

Formularies

00A30

数学哲学[参见03A05]

Philosophy of mathematics [See also 03A05]

00A35

数学方法论, 教学法[参见97Cxx, 97Dxx]

Methodology of mathematics, didactics [See also 97Cxx, 97Dxx]

00A65

数学和音乐

Mathematics and music

00A66

数学和视觉艺术, 可视化

Mathematics and visual arts, visualization

00A67

数学和建筑学

Mathematics and architecture

00A69

一般应用数学(物理, 00A7970-XX86-XX部分)

General applied mathematics (For physics, see 00A79 and Sections 70 through 86)

00A71

数学建模理论

Theory of mathematical modeling

00A72

一般模拟方法

General methods of simulation

00A73

维数分析

Dimensional analysis

00A79

物理学(尽可能使用从70-XX86-XX更明确的分类)

Physics (use more specific entries from Sections 70 through 86 when possible)

00A99

其它

Miscellaneous topics

00Bxx

会议录与论文集

Conference proceedings and collections of pa­pers

00B05

演讲摘要集

Collections of abstracts of lectures

00B10

一般论文集

Collections of articles of general interest

00B15

专题论文集

Collections of articles of miscellaneous specific content

00B20

一般会议录

Proceedings of conferences of general interest

00B25

专题会议录

Proceedings of conferences of miscellaneous specific interest

00B30

纪念文集

Festschriften

00B50

精选译文集

Volumes of selected translations

00B55

其它译文合订本

Miscellaneous volumes of translations

00B60

再版文集[参见01A75]

Collections of reprinted articles [See also 01A75]

00B99

其它

None of the above, but in this section

01-XX

历史与传记[参见其它一级类目中的分类号-03部分]

History and biography [See also the classifica­tion number -03 in the other sections]

01-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

01-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

01-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

01-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

01-08

计算方法

Computational methods

01Axx

数学史和数学家

History of mathematics and mathematicians

01A05

一般历史, 原始资料集

General histories, source books

01A07

民族数学, 一般问题

Ethnomathematics, general

01A10

旧石器时代, 新石器时代

Paleolithic, Neolithic

01A12

美洲土著文化

Indigenous cultures of the Americas

01A13

其它土著文化(非欧洲)

Other indigenous cultures (non-European)

01A15

欧洲土著文化(前希腊时期等)

Indigenous European cultures (pre-Greek, etc.)

01A16

埃及

Egyptian

01A17

巴比伦

Babylonian

01A20

希腊, 罗马

Greek, Roman

01A25

中国

China

01A27

日本

Japan

01A29

东南亚

Southeast Asia

01A30

伊斯兰(中世纪)

Islam (Medieval)

01A32

印度

India

01A35

中世纪

Medieval

01A40

15, 16世纪, 文艺复兴时期

15th and 16th centuries, Renaissance

01A45

17世纪

17th century

01A50

18世纪

18th century

01A55

19世纪

19th century

01A60

20世纪

20th century

01A61

21世纪

Twenty-first century

01A65

当代的

Contemporary

01A67

未来展望

Future prospectives

01A70

传记, 讣告, 轶事, 书目

Biographies, obituaries, personalia, bibliographies

01A72

数学学派

Schools of mathematics

01A73

大学

Universities

01A74

其它研究所和大专院校

Other institutions and academies

01A75

文集或选集; 经典著作的再版或翻译[参见00B60]

Collected or selected works; reprintings or translations of classics [See also 00B60]

01A80

数学社会学(和职业)

Sociology (and profession) of mathematics

01A85

历史书目

Historiography

01A90

书目研究

Bibliographic studies

01A99

其它

Miscellaneous topics

03-XX

数理逻辑与基础

Mathematical logic and foundations

03-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, biblio­graphies, etc.)

03-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

03-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

03-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

03-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

03-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

03Axx

逻辑和基础的哲学方面

Philosophical aspects of logic and foundations

03A05

哲学与评论(数学哲学, 参见00A30)

Philosophical and critical (For philosophy of mathematics, see also 00A30)

03A10

科学哲学中的逻辑

Logic in the philosophy of science

03A99

其它

None of the above, but in this section

03Bxx

一般逻辑

General logic

03B05

经典命题逻辑

Classical propositional logic

03B10

经典一阶逻辑

Classical first-order logic

03B15

高阶逻辑和类型论

Higher-order logic and type theory

03B20

经典逻辑子系统(包括直觉主义逻辑)

Subsystems of classical logic (including intuitionistic logic)

03B22

抽象演绎系统

Abstract deductive systems

03B25

理论的可判定性和命题集[参见11U05, 12L05, 20F10]

Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]

03B30

经典理论的基础(包括反演数学)[参见03F35]

Foundations of classical theories (including reverse mathe­matics) [See also 03F35]

03B35

证明和逻辑运算的机械化[参见68T15]

Mechanization of proofs and logical operations [See also 68T15]

03B40

组合逻辑和λ-演算[参见68N18]

Combinatory logic and lambda-calculus [See also 68N18]

03B42

知识和信仰的逻辑(包括信仰改变)

Logic of knowledge and belief (including belief change)

03B44

瞬时逻辑

Temporal logic

03B45

模态逻辑(包括标准逻辑)(知识和信仰逻辑, 03B42; 瞬时逻辑, 03B44; 可证明性逻辑, 参见03F45)

Modal logic (including the logic of norms) (For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45)

03B47

子结构逻辑(包括相关, 蕴涵, 线性逻辑, Lambek演算, BCKBCI逻辑)(证明论方面, 03F52)

Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (For proof-theoretic aspects, see 03F52)

03B48

概率和归纳逻辑[参见60A05]

Probability and inductive logic [See also 60A05]

03B50

多值逻辑

Many-valued logic

03B52

Fuzzy逻辑; 模糊逻辑[参见68T27, 68T37, 94D05]

Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]

03B53

仿相容逻辑

paraconsistent logics

03B55

中介逻辑

Intermediate logics

03B60

其它非经典逻辑

Other nonclassical logic

03B62

组合逻辑

Combined logics

03B65

自然语言逻辑[参见68T50, 91F20]

Logic of natural languages [See also 68T50, 91F20]

03B70

计算机科学中的逻辑[参见68-XX]

Logic in computer science [See also 68-XX]

03B80

逻辑的其它应用

Other applications of logic

03B99

其它

None of the above, but in this section

03Cxx

模型论

Model theory

03C05

等式类, 泛代数[参见08Axx, 08Bxx, 18C05]

Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]

03C07

一阶语言和结构的基本性质

Basic properties of first-order languages and structures

03C10

量词消去, 模型完备性和有关课题

Quantifier elimination, model completeness and related topics

03C13

有限结构[参见68Q15, 68Q19]

Finite structures [See also 68Q15, 68Q19]

03C15

可数结构

Denumerable structures

03C20

超积及有关构造

Ultraproducts and related constructions

03C25

模型论力迫

Model-theoretic forcing

03C30

其它模型构造

Other model constructions

03C35

理论的范畴性和完备性

Categoricity and completeness of theories

03C40

插值, 保存, 可定义性

Interpolation, preservation, definability

03C45

分类理论, 稳定性和有关概念[参见03C48]

Classification theory, stability and related concepts [See also 03C48]

03C48

抽象元素类及有关课题[参见03C45]

Abstract elementary classes and related topics [See also 03C45]

03C50

具有特殊性质的(饱和的、刚性的等)模型

Models with special properties (saturated, rigid, etc.)

03C52

模型类的性质

Properties of classes of models

03C55

集合论模型论

Set-theoretic model theory

03C57

有效和递归论模型论[参见03D45]

Effective and recursion-theoretic model theory [See also 03D45]

03C60

模型论代数[参见08C10, 12Lxx, 13L05]

Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]

03C62

算术模型与集合论模型[参见03Hxx]

Models of arithmetic and set theory [See also 03Hxx]

03C64

有序结构的模型论; o-极小性

Model theory of ordered structures; o-minimality

03C65

其它数学理论模型

Models of other mathematical theories

03C68

其它经典一阶模型论

Other classical first-order model theory

03C70

容许集上的逻辑

Logic on admissible sets

03C75

其它无穷逻辑

Other infinitary logic

03C80

有附加量词和算子的逻辑[参见03B42, 03B44, 03B45, 03B48]

Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]

03C85

二阶和高阶模型论

Second- and higher-order model theory

03C90

非经典模型(Boole值、层等)

Nonclassical models (Boolean-valued, sheaf, etc.)

03C95

抽象模型论

Abstract model theory

03C98

模型论的应用[参见03C60]

Applications of model theory [See also 03C60]

03C99

其它

None of the above, but in this section

03Dxx

可计算性和递归论

Computability and recursion theory

03D03

Thue系统和Post系统等

Thue and Post systems, etc.

03D05

与逻辑问题有关的自动机和形式语法[参见68Q45, 68Q70, 68R15]

Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]

03D10

Turing机和有关概念[参见68Q05]

Turing machines and related notions [See also 68Q05]

03D15

计算的复杂性(包括隐式计算复杂性)[参见68Q15, 68Q17]

Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17]

03D20

递归函数和关系, 次递归层级

Recursive functions and relations, subrecursive hierarchies

03D25

递归(可计算)可数集和度

Recursively (computably) enumerable sets and degrees

03D28

其它Turing度结构

Other Turing degree structures

03D30

其它度和可约性

Other degrees and reducibilities

03D32

算法随机性和维数[参见68Q30]

Algorithmic randomness and dimension [See also 68Q30]

03D35

命题集的不可判定性和度

Undecidability and degrees of sets of sentences

03D40

字问题等[参见06B25, 08A50, 20F10, 68R15]

Word problems, etc. [See also 06B25, 08A50, 20F10, 68R15]

03D45

记数法理论, 有效表述结构[参见03C57; 直觉主义及其相似的方法, 03F55]

Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]

03D50

集合和结构的递归等价类型, 孤点元

Recursive equivalence types of sets and structures, isols

03D55

谱系

Hierarchies

03D60

次序、容许集等的可计算性和递归论

Computability and recursion theory on ordinals, admissible sets, etc.

03D65

高阶递归和集递归理论

Higher-type and set recursion theory

03D70

归纳可定义性

Inductive definability

03D75

抽象公理化可计算性和递归理论

Abstract and axiomatic computability and recursion theory

03D78

实数计算(构造性方面, 03F60)

Computation over the reals (For constructive aspects, see 03F60)

03D80

可计算性和递归论的应用

Applications of computability and recursion theory

03D99

其它

None of the above, but in this section

03Exx

集合论

Set theory

03E02

分拆关系

Partition relations

03E04

有序集及其共尾性; pcf理论

Ordered sets and their cofinalities; pcf theory

03E05

其它组合集合论

Other combinatorial set theory

03E10

序数和基数

Ordinal and cardinal numbers

03E15

描述集合论[参见28A05, 54H05]

Descriptive set theory [See also 28A05, 54H05]

03E17

连续统的基数特征

Cardinal characteristics of the continuum

03E20

其它经典集合论(包括函数, 关系和集代数)

Other classical set theory (including functions, relations, and set algebra)

03E25

选择公理和有关命题

Axiom of choice and related propositions

03E30

经典集合论的公理体系及其若干方面

Axiomatics of classical set theory and its fragments

03E35

相容性和独立性的结果

Consistency and independence results

03E40

力迫和Boole值模型的其它方面

Other aspects of forcing and Boolean-valued models

03E45

内模型, 包括可构造性, 序数可定义性和核心模型

Inner models, including constructibility, ordinal defina­bility, and core models

03E47

集合论可定义性的其它概念

Other notions of set-theoretic definability

03E50

连续统假设和Martin公理[参见03E57]

Continuum hypothesis and Martin’s axiom [See also 03E57]

03E55

大基数

Large cardinals

03E57

一般绝对性和力迫公理[参见03E50]

Generic absoluteness and forcing axioms [See also 03E50]

03E60

确定性原理

Determinacy principles

03E65

其它假设和公理

Other hypotheses and axioms

03E70

非经典集合论和二阶集合论

Nonclassical and second-order set theories

03E72

模糊集论

Fuzzy set theory

03E75

集合论的应用

Applications of set theory

03E99

其它

None of the above, but in this section

03Fxx

证明论和构造性数学

Proof theory and constructive mathematics

03F03

证明论, 一般问题

Proof theory, general

03F05

切割-消去法和范式定理

Cut-elimination and normal-form theorems

03F07

证明的结构

Structure of proofs

03F10

证明论中的泛函

Functionals in proof theory

03F15

递归序数和序数记号

Recursive ordinals and ordinal notations

03F20

证明的复杂性

Complexity of proofs

03F25

有关相容性和解释

Relative consistency and interpretations

03F30

一阶算术及若干方面

First-order arithmetic and fragments

03F35

二阶和高阶算术及若干方面[参见03B30]

Second- and higher-order arithmetic and fragments [See also 03B30]

03F40

Gödel编号及不完全性问题

Gödel numberings and issues of incompleteness

03F45

可证明逻辑和相关代数(例如: 可对角化代数)[参见03B45, 03G25, 06E25]

Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]

03F50

构造系统元数学

Metamathematics of constructive systems

03F52

线性逻辑及其它子结构逻辑[参见03B47]

Linear logic and other substructural logics [See also 03B47]

03F55

直觉主义数学

Intuitionistic mathematics

03F60

构造性和递归分析[参见03B30, 03D45, 03D78, 26E40, 46S30, 47S30]

Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30]

03F65

其它构造性数学[参见03D45]

Other constructive mathematics [See also 03D45]

03F99

其它

None of the above, but in this section

03Gxx

代数逻辑

Algebraic logic

03G05

Boole代数[参见06Exx]

Boolean algebras [See also 06Exx]

03G10

格和有关结构[参见06Bxx]

Lattices and related structures [See also 06Bxx]

03G12

量子逻辑[参见06C15, 81P10]

Quantum logic [See also 06C15, 81P10]

03G15

柱型代数和多圆柱型代数; 关系代数

Cylindric and polyadic algebras; relation algebras

03G20

Łukasiewicz代数和Post代数[参见06D25, 06D30]

Łukasiewicz and Post algebras [See also 06D25, 06D30]

03G25

与逻辑有关的其它代数[参见03F45, 06D20, 06E25, 06F35]

Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]

03G27

抽象代数逻辑

Abstract algebraic logic

03G30

范畴逻辑, 普遍概念[参见18B25, 18C05, 18C10]

Categorical logic, topoi [See also 18B25, 18C05, 18C10]

03G99

其它

None of the above, but in this section

03Hxx

非标准模型[参见03C62]

Nonstandard models [See also 03C62]

03H05

数学中的非标准模型[参见26E35, 28E05, 30G06, 46S20, 47S20, 54J05]

Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]

03H10

非标准模型的其它应用(经济学、物理学等)

Other applications of nonstandard models (economics, physics, etc.)

03H15

算术的非标准模型[参见11U10, 12L15, 13L05]

Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]

03H99

其它

None of the above, but in this section

05-XX

组合学(有限域, 11Txx)

Combinatorics (For finite fields, see 11Txx)

05-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

05-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

05-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

05-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

05-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

05-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

05Axx

枚举组合学(图论中的枚举, 05C30)

Enumerative combinatorics (For enumeration in graph theory, see 05C30)

05A05

排列, , 矩阵

Permutations, words, matrices

05A10

阶乘, 二项式系数, 组合函数[参见11B65, 33Cxx]

Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]

05A15

精确枚举问题, 生成函数[参见33Cxx, 33Dxx]

Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

05A16

渐近枚举

Asymptotic enumeration

05A17

整数划分[参见11P81, 11P82, 11P83]

Partitions of integers [See also 11P81, 11P82, 11P83]

05A18

集合划分

Partitions of sets

05A19

组合恒等式, 双射组合学

Combinatorial identities, bijective combinatorics

05A20

组合不等式

Combinatorial inequalities

05A30

q-运算与有关课题[参见33Dxx]

q-calculus and related topics [See also 33Dxx]

05A40

哑运算

Umbral calculus

05A99

其它

None of the above, but in this section

05Bxx

设计与构形(设计理论的应用, 94C30)

Designs and configurations (For applications of design theory, see 94C30)

05B05

区组设计[参见51E05, 62K10]

Block designs [See also 51E05, 62K10]

05B07

三元系

Triple systems

05B10

差集(数论、群论等)[参见11B13]

Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]

05B15

正交阵列, Latin, Room

Orthogonal arrays, Latin squares, Room squares

05B20

矩阵(关联阵、Hadamard阵等)

Matrices (incidence, Hadamard, etc.)

05B25

有限几何[参见51D20, 51Exx]

Finite geometries [See also 51D20, 51Exx]

05B30

其它设计, 构形[参见51E30]

Other designs, configurations [See also 51E30]

05B35

拟阵, 几何格[参见52B40, 90C27]

Matroids, geometric lattices [See also 52B40, 90C27]

05B40

填装与覆盖[参见11H31, 52C15, 52C17]

Packing and covering [See also 11H31, 52C15, 52C17]

05B45

嵌图和贴砖问题[参见52C20, 52C22]

Tessellation and tiling problems [See also 52C20, 52C22]

05B50

多米诺骨牌

Polyominoes

05B99

其它

None of the above, but in this section

05Cxx

图论(图的应用, 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15)

Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15)

05C05

Trees

05C07

顶点度[参见05E30]

Vertex degrees [See also 05E30]

05C10

平面图; 图论的几何及拓扑方面[参见57M15, 57M25]

Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

05C12

图中距离

Distance in graphs

05C15

图和超图的着色

Coloring of graphs and hypergraphs

05C17

完美图

Perfect graphs

05C20

有向图, 竞赛图

Directed graphs (digraphs), tournaments

05C21

图中流

Flows in graphs

05C22

符号图和加权图

Signed and weighted graphs

05C25

图与抽象代数(群、环、域等)[参见20F65]

Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

05C30

图论中的枚举

Enumeration in graph theory

05C31

图多项式

Graph polynomials

05C35

极图问题[参见90C35]

Extremal problems [See also 90C35]

05C38

路和圈[参见90B10]

Paths and cycles [See also 90B10]

05C40

连通性

Connectivity

05C42

密度(韧性等)

Density (toughness, etc.)

05C45

Euler图和Hamilton

Eulerian and Hamiltonian graphs

05C50

图和线性代数(矩阵、特征值等)

Graphs and linear algebra (matrices, eigenvalues, etc.)

05C51

图设计与同构分解[参见05B30]

Graph designs and isomorphic decomposition [See also 05B30]

05C55

广义Ramsey理论[参见 05D10]

Generalized Ramsey theory [See also 05D10]

05C57

图上博弈[参见91A43, 91A46]

Games on graphs [See also 91A43, 91A46]

05C60

同构问题(重构猜想等)与同态(子图嵌入等)

Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)

05C62

图表示(几何和相交表示等)(图形制图, 参见68R10)

Graph representations (geometric and intersection representations, etc.) (For graph drawing, see also 68R10)

05C63

无限图

Infinite graphs

05C65

超图

Hypergraphs

05C69

控制集, 独立集,

Dominating sets, independent sets, cliques

05C70

因子, 匹配, 划分, 覆盖和填装

Factorization, matching, partitioning, covering and packing

05C72

分数图论, 模糊图论

Fractional graph theory, fuzzy graph theory

05C75

各种图族的结构特征

Structural characterization of families of graphs

05C76

图运算(线图、积等)

Graph operations (line graphs, products, etc.)

05C78

图标号(优美图、带宽等)

Graph labelling (graceful graphs, bandwidth, etc.)

05C80

随机图[参见 60B20]

Random graphs [See also 60B20]

05C81

图上随机游动

Random walks on graphs

05C82

小世界图, 复杂网络[参见90Bxx, 91D30]

Small world graphs, complex networks [See also 90Bxx, 91D30]

05C83

图子式

Graph minors

05C85

图算法[参见68R10, 68W05]

Graph algorithms [See also 68R10, 68W05]

05C90

应用[参见68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]

Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]

05C99

其它

None of the above, but in this section

05Dxx

极值组合学

Extremal combinatorics

05D05

极值集合论

Extremal set theory

05D10

Ramsey理论[参见05C55]

Ramsey theory [See also 05C55]

05D15

横截(匹配)理论

Transversal (matching) theory

05D40

概率方法

Probabilistic methods

05D99

其它

None of the above, but in this section

05Exx

代数组合学

Algebraic combinatorics

05E05

对称函数和推广

Symmetric functions and generalizations

05E10

表示理论的组合方面[参见20C30]

Combinatorial aspects of representation theory [See also 20C30]

05E15

群和代数的组合方面[参见14Nxx, 22E45, 33C80]

Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]

05E18

组合结构上的群作用

Group actions on combinatorial structures

05E30

结合概型, 强正则图

Association schemes, strongly regular graphs

05E40

交换代数的组合方面

Combinatorial aspects of commutative algebra

05E45

单纯复形的组合方面

Combinatorial aspects of simplicial complexes

05E99

其它

None of the above, but in this section

06-XX

, , 有序的代数结构[参见18B35]

Order, lattices, ordered algebraic struc­tures [See also 18B35]

06-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

06-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

06-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

06-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

06-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

06-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

06Axx

有序集

Ordered sets

06A05

全序

Total order

06A06

偏序, 一般问题

Partial order, general

06A07

偏序集组合学

Combinatorics of partially ordered sets

06A11

偏序集的代数方面

Algebraic aspects of posets

06A12

半格[参见20M10; 拓扑半格, 22A26]

Semilattices [See also 20M10; for topological semilattices see 22A26]

06A15

Galois对应, 闭包算子

Galois correspondences, closure operators

06A75

有序集的推广

Generalizations of ordered sets

06A99

其它

None of the above, but in this section

06Bxx

[参见03G10]

Lattices [See also 03G10]

06B05

结构理论

Structure theory

06B10

理想, 同余关系

Ideals, congruence relations

06B15

表示理论

Representation theory

06B20

格簇

Varieties of lattices

06B23

完备格, 完备化

Complete lattices, completions

06B25

自由格, 射影格, 字问题[参见03D40, 08A50, 20F10]

Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]

06B30

拓扑格, 序拓扑[参见06F30, 22A26, 54F05, 54H12]

Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]

06B35

连续格和偏序集, 应用[参见06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]

Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]

06B75

格的推广

Generalizations of lattices

06B99

其它

None of the above, but in this section

06Cxx

模格, 补格

Modular lattices, complemented lattices

06C05

模格, Desargues

Modular lattices, Desarguesian lattices

06C10

半模格, 几何格

Semimodular lattices, geometric lattices

06C15

补格, 正交补格和偏序集[参见03G12, 81P10]

Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]

06C20

补模格, 连续几何

Complemented modular lattices, continuous geometries

06C99

其它

None of the above, but in this section

06Dxx

分配格

Distributive lattices

06D05

结构与表示理论

Structure and representation theory

06D10

完全分配性

Complete distributivity

06D15

伪补格

Pseudocomplemented lattices

06D20

Heyting代数[参见03G25]

Heyting algebras [See also 03G25]

06D22

框架, 场所(拓扑问题见54-XX)

Frames, locales (For topological questions see 54-XX)

06D25

Post代数[参见03G20]

Post algebras [See also 03G20]

06D30

De Morgan代数, Łukasiewicz代数[参见03G20]

De Morgan algebras, Łukasiewicz algebras [See also 03G20]

06D35

MV-代数

MV-algebras

06D50

格和对偶性

Lattices and duality

06D72

Fuzzy(软代数)和相关课题

Fuzzy lattices (soft algebras) and related topics

06D75

分配格的其它推广

Other generalizations of distributive lattices

06D99

其它

None of the above, but in this section

06Exx

Boole代数(Boole)[参见03G05]

Boolean algebras (Boolean rings) [See also 03G05]

06E05

结构理论

Structure theory

06E10

链条件, 完备代数

Chain conditions, complete algebras

06E15

Stone空间(Boole空间)和有关构造

Stone space (Boolean spaces) and related constructions

06E20

环理论性质[参见16E50, 16G30]

Ring-theoretic properties [See also 16E50, 16G30]

06E25

有加法运算的Boole代数(可对角化代数等)[参见03G25, 03F45]

Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]

06E30

Boole函数[参见94C10]

Boolean functions [See also 94C10]

06E75

Boole代数的推广

Generalizations of Boolean algebras

06E99

其它

None of the above, but in this section

06Fxx

有序结构

Ordered structures

06F05

有序半群和幺半群[参见20Mxx]

Ordered semigroups and monoids [See also 20Mxx]

06F07

局量子

Quantales

06F10

Noether

Noether lattices

06F15

有序群[参见20F60]

Ordered groups [See also 20F60]

06F20

有序Abel, Riesz, 有序线性空间[参见46A40]

Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]

06F25

有序环, 有序代数, 有序模(有序域, 12J15; 参见13J25, 16W80)

Ordered rings, algebras, modules (For ordered fields, see 12J15; see also 13J25, 16W80)

06F30

拓扑格, 序拓扑[参见06B30, 22A26, 54F05, 54H12]

Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]

06F35

BCK-代数, BCI-代数[参见03G25]

BCK-algebras, BCI-algebras [See also 03G25]

06F99

其它

None of the above, but in this section

08-XX

一般代数系统

General algebraic systems

08-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, biblio­graphies, etc.)

08-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

08-02

研究阐述(教著, 评述论文)

Research exposition (monographs, survey articles)

08-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

08-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

08-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

08Axx

代数结构[参见03C05]

Algebraic structures [See also 03C05]

08A02

关系系统, 合成定律

Relational systems, laws of composition

08A05

结构理论

Structure theory

08A30

子代数, 同余关系

Subalgebras, congruence relations

08A35

自同构, 自同态

Automorphisms, endomorphisms

08A40

运算, 多项式, 初等代数

Operations, polynomials, primal algebras

08A45

等价紧性

Equational compactness

08A50

字问题[参见03D40, 06B25, 20F10, 68R15]

Word problems [See also 03D40, 06B25, 20F10, 68R15]

08A55

偏代数

Partial algebras

08A60

一元代数

Unary algebras

08A62

有限代数

Finitary algebras

08A65

无限代数

Infinitary algebras

08A68

非纯一代数

Heterogeneous algebras

08A70

泛代数在计算机科学中的应用

Applications of universal algebra in computer science

08A72

Fuzzy代数结构

Fuzzy algebraic structures

08A99

其它

None of the above, but in this section

08Bxx

[参见03C05]

Varieties [See also 03C05]

08B05

等价逻辑, Mal'cev (Mal'tsev)条件

Equational logic, Mal'cev (Mal'tsev) conditions

08B10

同余模性, 同余分配性

Congruence modularity, congruence distributivity

08B15

簇格

Lattices of varieties

08B20

自由代数

Free algebras

08B25

, 融和积, 各种极限和上极限[参见18A30]

Products, amalgamated products, and other kinds of limits and colimits [See also 18A30]

08B26

次直积与次直不可约性

Subdirect products and subdirect irreducibility

08B30

内射, 射影

Injectives, projectives

08B99

其它

None of the above, but in this section

08Cxx

其它代数类

Other classes of algebras

08C05

代数范畴[参见18C05]

Categories of algebras [See also 18C05]

08C10

公理化模型类[参见03Cxx, 特别见03C60]

Axiomatic model classes [See also 03Cxx, in particular 03C60]

08C15

拟簇

Quasivarieties

08C20

代数类的自然对偶性[参见06E15, 18A40, 22A30]

Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30]

08C99

其它

None of the above, but in this section

11-XX

数论

Number theory

11-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

11-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

11-02

研究阐述(教著, 评述论文)

Research exposition (monographs, survey articles)

11-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

11-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

11-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

11Axx

初等数论(数域中的模拟, 11R04)

Elementary number theory (For analogues in num­ber fields, see 11R04)

11A05

乘法结构; Euclid算法; 最大公约数

Multiplicative structure; Euclidean algorithm; greatest common divisors

11A07

同余; 原根; 剩余系

Congruences; primitive roots; residue systems

11A15

幂剩余, 互反性

Power residues, reciprocity

11A25

算术函数; 相关数; 反演公式

Arithmetic functions; related numbers; inversion formulas

11A41

素数

Primes

11A51

因子分解; 基本性质

Factorization; primality

11A55

连分数(近似结果, 11J70)[参见11K50, 30B70, 40A15]

Continued fractions (For approximation results, see 11J70) [See also 11K50, 30B70, 40A15]

11A63

基数表示; 数字问题(度量结果, 11K16)

Radix representation; digital problems (For metric results, see 11K16)

11A67

其它表示

Other representations

11A99

其它

None of the above, but in this section

11Bxx

序列与集合

Sequences and sets

11B05

稠密性, 间隙, 拓扑

Density, gaps, topology

11B13

加性基, 包括和集[参见05B10]

Additive bases, including sumsets [See also 05B10]

11B25

算术级数[参见11N13]

Arithmetic progressions [See also 11N13]

11B30

算术组合学; 高度一致性

Arithmetic combinatorics; higher degree uniformity

11B34

表示函数

Representation functions

11B37

递归(特殊函数的应用, 33-XX)

Recurrences (For applications to special functions, see 33-XX)

11B39

Fibonacci, Lucas, 多项式及推广

Fibonacci and Lucas numbers and polynomials and generalizations

11B50

序列(m)

Sequences (mod m)

11B57

Farey序列; 序列1k, 2k, …

Farey sequences; the sequences 1k, 2k, …

11B65

二项式系数; 阶乘; q-恒等式[参见05A10, 05A30]

Binomial coefficients; factorials; q-identities [See also 05A10, 05A30]

11B68

Bernoulli, Euler数和多项式

Bernoulli and Euler numbers and polynomials

11B73

Bell数和Stirling

Bell and Stirling numbers

11B75

其它组合数论

Other combinatorial number theory

11B83

特殊序列和多项式

Special sequences and polynomials

11B85

自动机序列

Automata sequences

11B99

其它

None of the above, but in this section

11Cxx

多项式和矩阵

Polynomials and matrices

11C08

多项式[参见13F20]

Polynomials [See also 13F20]

11C20

矩阵, 行列式[参见15B36]

Matrices, determinants [See also 15B36]

11C99

其它

None of the above, but in this section

11Dxx

Diophantus方程[参见11Gxx, 14Gxx]

Diophantine equations [See also 11Gxx, 14Gxx]

11D04

线性方程

Linear equations

11D07

Frobenius问题

The Frobenius problem

11D09

二次方程和双线性方程

Quadratic and bilinear equations

11D25

三次方程和四次方程

Cubic and quartic equations

11D41

高次方程; Fermat方程

Higher degree equations; Fermat’s equation

11D45

Diophantus方程的计数解

Counting solutions of Diophantine equations

11D57

乘法方程和范数形式方程

Multiplicative and norm form equations

11D59

Thue-Mahler方程

Thue-Mahler equations

11D61

指数方程

Exponential equations

11D68

可作为分数和的有理数

Rational numbers as sums of fractions

11D72

多变量方程[参见11P55]

Equations in many variables [See also 11P55]

11D75

Diophantus不等式[参见11J25]

Diophantine inequalities [See also 11J25]

11D79

多变量同余

Congruences in many variables

11D85

表示问题[参见11P55]

Representation problems [See also 11P55]

11D88

p-进域和幂级数域

p-adic and power series fields

11D99

其它

None of the above, but in this section

11Exx

型和线性代数群[参见19Gxx](线性代数二次型, 15A63)

Forms and linear algebraic groups [See also 19Gxx] (For quadratic forms in linear algebra, see 15A63)

11E04

一般域上的二次型

Quadratic forms over general fields

11E08

局部环和局部域上的二次型

Quadratic forms over local rings and fields

11E10

实域上的型

Forms over real fields

11E12

整体环和整体域上的二次型

Quadratic forms over global rings and fields

11E16

一般双元二次型

General binary quadratic forms

11E20

一般三元和四元二次型; 多于两个变量的型

General ternary and quaternary quadratic forms; forms of more than two variables

11E25

平方和及其它特殊二次型的表示

Sums of squares and representations by other particular quadratic forms

11E39

双线性型和Hermite

Bilinear and Hermitian forms

11E41

二次型和Hermite型的类数

Class numbers of quadratic and Hermitian forms

11E45

解析理论(Epstein ζ函数; 与自同构型和函数的关系)

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)

11E57

典型群[参见14Lxx, 20Gxx]

Classical groups [See also 14Lxx, 20Gxx]

11E70

二次型与Hermite型的K-理论

K-theory of quadratic and Hermitian forms

11E72

线性代数群的Galois上同调[参见20G10]

Galois cohomology of linear algebraic groups [See also 20G10]

11E76

高于二次的型

Forms of degree higher than two

11E81

二次型的代数理论; Witt群和环[参见19G12, 19G24]

Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]

11E88

二次空间; Clifford代数[参见15A63, 15A66]

Quadratic spaces; Clifford algebras [See also 15A63, 15A66]

11E95

p-进理论

p-adic theory

11E99

其它

None of the above, but in this section

11Fxx

不连续群和自守形式[参见11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx](与二次型的关系, 11E45)

Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] (For relations with quadratic forms, see 11E45)

11F03

模函数和自守函数

Modular and automorphic functions

11F06

模群的结构和推广; 算术群[参见20H05, 20H10, 22E40]

Structure of modular groups and generalizations; arith­metic groups [See also 20H05, 20H10, 22E40]

11F11

积分权重的全纯模形式

Holomorphic modular forms of integral weight

11F12

自守形式, 单变量

Automorphic forms, one variable

11F20

Dedekind η函数, Dedekind

Dedekind eta function, Dedekind sums

11F22

Lie代数和有限单群的关系

Relationship to Lie algebras and finite simple groups

11F23

与代数几何和拓扑的关系

Relations with algebraic geometry and topology

11F25

Hecke-Petersson算子, 微分算子(单变量)

Hecke-Petersson operators, differential operators (one variable)

11F27

θ级数; Weil表示;θ对应

Theta series; Weil representation; theta correspondences

11F30

自守形式的Fourier系数

Fourier coefficients of automorphic forms

11F32

模对应等

Modular correspondences, etc.

11F33

模和p-进模形式的同余[参见14G20, 22E50]

Congruences for modular and p-adic modular forms [See also 14G20, 22E50]

11F37

半整数加权形式; 非全纯模形式

Forms of half-integer weight; nonholomorphic modular forms

11F41

GL(2)上的自守形式; HilbertHilbert-Siegel模群及其模形式和自守形式; Hilbert模曲面[参见14J20]

Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]

11F46

Siegel模群; SiegelHilbert-Siegel模形式和自守形式

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

11F50

Jacobi形式

Jacobi forms

11F52

Drinfel'd模有关的模形式

Modular forms associated to Drinfel'd modules

11F55

其它群及其模形式和自守形式(多变量)

Other groups and their modular and automorphic forms (several variables)

11F60

Hecke-Petersson算子, 微分算子(多变量)

Hecke-Petersson operators, differential operators (several variables)

11F66

Langlands L-函数;单变量Diri­chlet级数和泛函方程

Langlands L-functions; one variable Dirichlet series and functional equations

11F67

自守L-级数的特殊值, 模形式的周期, 上同调, 模符号

Special values of automorphic L-series, periods of modular forms, cohomology, modular symbols

11F68

多复变量中与自守形式相关的Dirichlet级数; Weyl群多重Diri­chlet级数

Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series

11F70

表示理论的方法; 局部域和整体域上的自守表示

Representation-theoretic methods; automorphic represen­tations over local and global fields

11F72

谱理论; Selberg迹公式

Spectral theory; Selberg trace formula

11F75

算术群的上同调

Cohomology of arithmetic groups

11F80

Galois表示

Galois representations

11F85

p-进理论, 局部域[参见14G20, 22E50]

p-adic theory, local fields [See also 14G20, 22E50]

11F99

其它

None of the above, but in this section

11Gxx

算术代数几何(Diophantus几何)[参见11Dxx, 14Gxx, 14Kxx]

Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]

11G05

整体域上的椭圆曲线[参见14H52]

Elliptic curves over global fields [See also 14H52]

11G07

局部域上的椭圆曲线[参见14G20, 14H52]

Elliptic curves over local fields [See also 14G20, 14H52]

11G09

Drinfel'd; 高维运动等[参见14L05]

Drinfel'd modules; higher-dimensional motives, etc. [See also 14L05]

11G10

维数>1Abel[参见14Kxx]

Abelian varieties of dimension >1 [See also 14Kxx]

11G15

Abel簇的复数乘法和模数[参见14K22]

Complex multiplication and moduli of abelian varieties [See also 14K22]

11G16

椭圆单位和模单位[参见11R27]

Elliptic and modular units [See also 11R27]

11G18

模和Shimura簇的算术方面[参见14G35]

Arithmetic aspects of modular and Shimura varieties [See also 14G35]

11G20

有限域和局部域上的曲线[参见14H25]

Curves over finite and local fields [See also 14H25]

11G25

有限域和局部域上的簇[参见14G15, 14G20]

Varieties over finite and local fields [See also 14G15, 14G20]

11G30

整体域上任意亏格或亏格≠1的曲线[参见14H25]

Curves of arbitrary genus or genus ≠1 over global fields [See also 14H25]

11G32

Dessins d'enfants, Belyǐ理论

Dessins d'enfants, Belyǐ theory

11G35

整体域上的簇[参见14G25]

Varieties over global fields [See also 14G25]

11G40

整体域上簇的L-函数; Birch-Swinnerton-Dyer猜想[参见14G10]

L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]

11G42

算术镜对称[参见14J33]

Arithmetic mirror symmetry [See also 14J33]

11G45

几何类域理论[参见11R37, 14C35, 19F05]

Geometric class field theory [See also 11R37, 14C35, 19F05]

11G50

高度[参见14G40, 37P30]

Heights [See also 14G40, 37P30]

11G55

多对数及与K-理论的关系

Polylogarithms and relations with K-theory

11G99

其它

None of the above, but in this section

11Hxx

数的几何(在编码理论中的应用, 94B75)

Geometry of numbers (For applications in coding theory, see 94B75)

11H06

格与凸体[参见11P21, 52C05, 52C07]

Lattices and convex bodies [See also 11P21, 52C05, 52C07]

11H16

非凸体

Nonconvex bodies

11H31

格填装与覆盖[参见05B40, 52C15, 52C17]

Lattice packing and covering [See also 05B40, 52C15, 52C17]

11H46

线性型的积

Products of linear forms

11H50

型的极小值

Minima of forms

11H55

二次型(约化理论、极型等)

Quadratic forms (reduction theory, extreme forms, etc.)

11H56

格的自同构群

Automorphism groups of lattices

11H60

均值与转移定理

Mean value and transfer theorems

11H71

与编码理论的关系

Relations with coding theory

11H99

其它

None of the above, but in this section

11Jxx

Diophantus逼近, 超越数理论[参见11K60]

Diophantine approximation, transcendental number theory [See also 11K60]

11J04

一个数的齐次逼近

Homogeneous approximation to one number

11J06

Markov谱和Lagrange谱及推广

Markov and Lagrange spectra and generalizations

11J13

联立齐次逼近, 线性型

Simultaneous homogeneous approximation, linear forms

11J17

固定域中数逼近

Approximation by numbers from a fixed field

11J20

非齐次线性型

Inhomogeneous linear forms

11J25

Diophantus不等式[参见11D75]

Diophantine inequalities [See also 11D75]

11J54

多项式小分式部分及推广

Small fractional parts of polynomials and generalizations

11J61

Archimedes赋值中的逼近

Approximation in non-Archimedean valuations

11J68

代数数逼近

Approximation to algebraic numbers

11J70

连分数及推广[参见11A55, 11K50]

Continued fractions and generalizations [See also 11A55, 11K50]

11J71

分布模1[参见11K06]

Distribution modulo one [See also 11K06]

11J72

无理性; 域上的线性独立性

Irrationality; linear independence over a field

11J81

超越性(一般理论)

Transcendence (general theory)

11J82

无理性和超越性的测度

Measures of irrationality and of transcendence

11J83

度量理论

Metric theory

11J85

代数独立性; Gel'fond方法

Algebraic independence; Gel'fond’s method

11J86

对数中的线性型; Baker方法

Linear forms in logarithms; Baker’s method

11J87

Schmidt子空间定理及应用

Schmidt subspace theorem and applications

11J89

椭圆函数和Abel函数的超越理论

Transcendence theory of elliptic and abelian functions

11J91

其它特殊函数的超越理论

Transcendence theory of other special functions

11J93

Drinfel'dt-模的超越理论

Transcendence theory of Drinfel'd and t-modules

11J95

涉及Abel簇的结果

Results involving abelian varieties

11J97

Nevanlinna理论中方法的模拟(Vojta等的工作)

Analogues of methods in Nevanlinna theory (work of Vojta et al.)

11J99

其它

None of the above, but in this section

11Kxx

概率理论: 分布模1; 算法度量理论

Probabilistic theory: distribution modulo 1; metric theory of algorithms

11K06

分布模1的一般理论[参见11J71]

General theory of distribution modulo 1 [See also 11J71]

11K16

正规数, 基数展开, Pisot, Salem, 好格点等[参见11A63]

Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]

11K31

特殊序列

Special sequences

11K36

Well分布序列和其它变差

Well-distributed sequences and other variations

11K38

分布的不规则性, 不一致性[参见11Nxx]

Irregularities of distribution, discrepancy [See also 11Nxx]

11K41

连续, p-进和抽象模拟

Continuous, p-adic and abstract analogues

11K45

伪随机数; Monte Carlo方法

Pseudo-random numbers; Monte Carlo methods

11K50

连分数度量理论[参见11A55, 11J70]

Metric theory of continued fractions [See also 11A55, 11J70]

11K55

其它算法的度量理论和展开; 测度与Hausdorff维数[参见11N99, 28Dxx]

Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]

11K60

Diophantus逼近[参见11Jxx]

Diophantine approximation [See also 11Jxx]

11K65

算术函数[参见11Nxx]

Arithmetic functions [See also 11Nxx]

11K70

调和分析与殆周期性

Harmonic analysis and almost periodicity

11K99

其它

None of the above, but in this section

11Lxx

指数和与特征和(有限域, 11Txx)

Exponential sums and character sums (For finite fields, see 11Txx)

11L03

三角和与指数和, 一般问题

Trigonometric and exponential sums, general

11L05

Gauss和与Kloosterman; 推广

Gauss and Kloosterman sums; generalizations

11L07

指数和估计

Estimates on exponential sums

11L10

Jacobsthal和与Brewer; 其它完备特征和

Jacobsthal and Brewer sums; other complete character sums

11L15

Wey1

Weyl sums

11L20

素数上的和

Sums over primes

11L26

任意区间上的和

Sums over arbitrary intervals

11L40

特征和的估计

Estimates on character sums

11L99

其它

None of the above, but in this section

11Mxx

ζ函数与L-函数: 解析理论

Zeta and L-functions: analytic theory

11M06

ζ(s)L(s, χ)

ζ(s) and L(s, χ)

11M20

L(s, χ)的实零点; 关于L(1, χ)的结果

Real zeros of L(s, χ); results on L(1, χ)

11M26

ζ(s)L(s, χ)的非实零点; Riemann和其它假设

Nonreal zeros ofζ(s) and L(s, χ); Riemann and other hypotheses

11M32

多重 Dirichlet级数和ζ函数以及多ζ

Multiple Dirichlet series and zeta functions and multizeta values

11M35

HurwitzLerch ζ函数

Hurwitz and Lerch zeta functions

11M36

Selberg ζ函数和正则化行列式; 应用于谱论、Dirichlet级数、Eisenstein级数等显式公式

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. explicit formulas

11M38

特征p中的ζ函数和L-函数

Zeta and L-functions in characteristic p

11M41

其它Dirichlet级数与ζ函数(局部和整体基本域, 11R42, 11R52, 11S40, 11S45; 代数几何方法, 14G10; 参见11E45, 11F66, 11F70, 11F72)

Other Dirichlet series and zeta functions (For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72)

11M45

Tauber定理[参见40E05]

Tauberian theorems [See also 40E05]

11M50

与随机矩阵的关系

Relations with random matrices

11M55

与非交换几何的关系

Relations with noncommutative geometry

11M99

其它

None of the above, but in this section

11Nxx

乘法数论

Multiplicative number theory

11N05

素数分布

Distribution of primes

11N13

级数中的素数[参见11B25]

Primes in progressions [See also 11B25]

11N25

带特殊乘法约束的整数分布

Distribution of integers with specified multiplicative constraints

11N30

Turán理论[参见30Bxx]

Turán theory [See also 30Bxx]

11N32

用多项式表示的素数; 多项式值的其它乘法结构

Primes represented by polynomials; other multiplicative structure of polynomial values

11N35

筛法

Sieves

11N36

筛法的应用

Applications of sieve methods

11N37

算术函数的渐近结果

Asymptotic results on arithmetic functions

11N45

代数与拓扑结构的计数函数的渐近结果

Asymptotic results on counting functions for algebraic and topological structures

11N56

算术函数的增长率

Rate of growth of arithmetic functions

11N60

与加法和正乘法函数相关的分布函数

Distribution functions associated with additive and positive multiplicative functions

11N64

算术函数的值分布或特征的其它结果

Other results on the distribution of values or the characterization of arithmetic functions

11N69

特殊剩余类中的整数分布

Distribution of integers in special residue classes

11N75

自守函数与型在乘法问题中的应用[参见11Fxx]

Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]

11N80

广义素数与整数

Generalized primes and integers

11N99

其它

None of the above, but in this section

11Pxx

堆垒数论; 划分

Additive number theory; partitions

11P05

Waring问题及变量

Waring’s problem and variants

11P21

特殊区域中的格点

Lattice points in specified regions

11P32

Goldbach型定理; 包含素数的其它堆垒问题

Goldbach-type theorems; other additive questions involving primes

11P55

Hardy-Littlewood方法的应用[参见11D85]

Applications of the Hardy-Littlewood method [See also 11D85]

11P70

堆垒数论的逆问题, 包括和集

Inverse problems of additive number theory, including sumsets

11P81

划分的基本理论[参见05A17]

Elementary theory of partitions [See also 05A17]

11P82

划分的解析理论

Analytic theory of partitions

11P83

划分; 同余和同余限制

Partitions; congruences and congruential restrictions

11P84

划分恒等式; Rogers-Ramanujan型恒等式

Partition identities; identities of Rogers-Ramanujan type

11P99

其它

None of the above, but in this section

11Rxx

代数数论: 整体域(复数乘法, 11G15)

Algebraic number theory: global fields (For complex multiplication, see 11G15)

11R04

代数数; 代数整数环

Algebraic numbers; rings of algebraic integers

11R06

PV数及其推广; 其它特殊的代数数; Mahler测度

PV-numbers and generalizations; other special algebraic numbers; Mahler measure

11R09

多项式(不可约性等)

Polynomials (irreducibility, etc.)

11R11

二次扩张

Quadratic extensions

11R16

三次和四次扩张

Cubic and quartic extensions

11R18

割圆扩张

Cyclotomic extensions

11R20

其它Abel扩张与亚Abel扩张

Other abelian and metabelian extensions

11R21

其它数域

Other number fields

11R23

Iwasawa理论

Iwasawa theory

11R27

单位与因式分解

Units and factorization

11R29

类数, 类群, 判别式

Class numbers, class groups, discriminants

11R32

Galois理论

Galois theory

11R33

关于代数数的整数表示; 整数环的Galois模结构[参见20C10]

Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]

11R34

Galois上同调[参见12Gxx, 19A31]

Galois cohomology [See also 12Gxx, 19A31]

11R37

类域理论

Class field theory

11R39

Langlands-Weil猜想, Abel类域理论[参见11Fxx, 22E55]

Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]

11R42

数域的ζ函数和L-函数[参见11M41, 19F27]

Zeta functions and L-functions of number fields [See also 11M41, 19F27]

11R44

素理论分布[参见11N05]

Distribution of prime ideals [See also 11N05]

11R45

密度定理

Density theorems

11R47

其它解析理论[参见11Nxx]

Other analytic theory [See also 11Nxx]

11R52

四元数与其它可除代数: 算术, ζ函数

Quaternion and other division algebras: arithmetic, zeta functions

11R54

其它代数与整环, 及其ζ函数与L-函数[参见11S45, 16H05, 16Kxx]

Other algebras and orders, and their zeta and L-functions [See also 11S45, 16H05, 16Kxx]

11R56

Adèle环与群

Adèle rings and groups

11R58

代数函数域的算术理论[参见14-XX]

Arithmetic theory of algebraic function fields [See also 14-XX]

11R60

割圆函数域(类群、Bernoulli目标等)

Cyclotomic function fields (class groups, Bernoulli objects, etc.)

11R65

整环的类群和Picard

Class groups and Picard groups of orders

11R70

整体域的K-理论[参见19Fxx]

K-theory of global fields [See also 19Fxx]

11R80

全实域[参见12J15]

Totally real fields [See also 12J15]

11R99

其它

None of the above, but in this section

11Sxx

代数数论: 局部域和p-进域

Algebraic number theory: local and p-adic fields

11S05

多项式

Polynomials

11S15

分歧与扩张理论

Ramification and extension theory

11S20

Galois理论

Galois theory

11S23

整数表示

Integral representations

11S25

Galois上同调[参见12Gxx, 16H05]

Galois cohomology [See also 12Gxx, 16H05]

11S31

类域理论; p-进形式群[参见14L05]

Class field theory; p-adic formal groups [See also 14L05]

11S37

Langlands-Weil猜想, Abel类域理论[参见11Fxx, 22E50]

Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]

11S40

ζ函数与L-函数[参见11M41, 19F27]

Zeta functions and L-functions [See also 11M41, 19F27]

11S45

代数和整环, 及其ζ函数[参见11R52, 11R54, 16Hxx, 16Kxx]

Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx]

11S70

局部域的K-理论[参见19Fxx]

K-theory of local fields [See also 19Fxx]

11S80

其它解析理论(β函数和Γ函数的模拟、p-进积分法等)

Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)

11S82

Archimedes动力系统[主要见 37Pxx]

Non-Archimedean dynamical systems [See mainly 37Pxx]

11S85

其它非解析理论

Other nonanalytic theory

11S90

准齐性向量空间

Prehomogeneous vector spaces

11S99

其它

None of the above, but in this section

11Txx

有限域和有限交换环(数论方面)

Finite fields and commutative rings (number-theoretic aspects)

11T06

多项式

Polynomials

11T22

割圆

Cyclotomy

11T23

指数和

Exponential sums

11T24

其它特征和与高斯和

Other character sums and Gauss sums

11T30

结构理论

Structure theory

11T55

有限域上多项式环的算术理论

Arithmetic theory of polynomial rings over finite fields

11T60

有限上半平面

Finite upper half-planes

11T71

代数编码理论; 密码学

Algebraic coding theory; cryptography

11T99

其它

None of the above, but in this section

11Uxx

与逻辑的联系

Connections with logic

11U05

可判定性[参见03B25]

Decidability [See also 03B25]

11U07

超积[参见03C20]

Ultraproducts [See also 03C20]

11U09

模型论[参见03Cxx]

Model theory [See also 03Cxx]

11U10

非标准算术[参见03H15]

Nonstandard arithmetic [See also 03H15]

11U99

其它

None of the above, but in this section

11Yxx

计算数论[参见11-04]

Computational number theory [See also 11-04]

11Y05

因子分解

Factorization

11Y11

基本性质

Primality

11Y16

算法; 复杂性[参见68Q25]

Algorithms; complexity [See also 68Q25]

11Y35

解析计算

Analytic computations

11Y40

代数数论计算

Algebraic number theory computations

11Y50

Diophantus方程的计算机解

Computer solution of Diophantine equations

11Y55

整数序列的计算

Calculation of integer sequences

11Y60

常数的赋值

Evaluation of constants

11Y65

连分式计算

Continued fraction calculations

11Y70

算术函数值; 表格

Values of arithmetic functions; tables

11Y99

其它

None of the above, but in this section

11Zxx

数论的其它应用

Miscellaneous applications of number theory

11Z05

数论的其它应用

Miscellaneous applications of number theory

11Z99

其它

None of the above, but in this section

12-XX

域论和多项式

Field theory and polynomials

12-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

12-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

12-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

12-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

12-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

12-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

12Dxx

实域和复域

Real and complex fields

12D05

多项式: 因式分解

Polynomials: factorization

12D10

多项式: 零点的位置(代数定理)(解析理论, 26C10, 30C15)

Polynomials: location of zeros (algebraic theorems) (For the analytic theory, see 26C10, 30C15)

12D15

与平方和有关的域(形式实域、Pythagoras域等)[参见11Exx]

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]

12D99

其它

None of the above, but in this section

12Exx

一般域论

General field theory

12E05

多项式(不可约性等)

Polynomials (irreducibility, etc.)

12E10

特殊多项式

Special polynomials

12E12

方程

Equations

12E15

斜域, 除环[参见11R52, 11R54, 11S45, 16Kxx]

Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]

12E20

有限域(域论方面)

Finite fields (field-theoretic aspects)

12E25

Hilbert; Hilbert不可约性定理

Hilbertian fields; Hilbert’s irreducibility theorem

12E30

域算术

Field arithmetic

12E99

其它

None of the above, but in this section

12Fxx

域扩张

Field extensions

12F05

代数扩张

Algebraic extensions

12F10

可分扩张, Galois理论

Separable extensions, Galois theory

12F12

Galois理论

Inverse Galois theory

12F15

不可分扩张

Inseparable extensions

12F20

超越扩张

Transcendental extensions

12F99

其它

None of the above, but in this section

12Gxx

同调方法(域论)

Homological methods (field theory)

12G05

Galois上同调[参见14F22, 16Hxx, 16K50]

Galois cohomology [See also 14F22, 16Hxx, 16K50]

12G10

上同调维数

Cohomological dimension

12G99

其它

None of the above, but in this section

12Hxx

微分代数与差分代数

Differential and difference algebra

12H05

微分代数[参见13Nxx]

Differential algebra [See also 13Nxx]

12H10

差分代数[参见39Axx]

Difference algebra [See also 39Axx]

12H20

抽象微分方程[参见34Mxx]

Abstract differential equations [See also 34Mxx]

12H25

p-进微分方程[参见11S80, 14G20]

p-adic differential equations [See also 11S80, 14G20]

12H99

其它

None of the above, but in this section

12Jxx

拓扑域

Topological fields

12J05

赋范域

Normed fields

12J10

值域

Valued fields

12J12

形式p-进域

Formally p-adic fields

12J15

有序域

Ordered fields

12J17

扑拓半域

Topological semifields

12J20

一般赋值理论[参见13A18]

General valuation theory [See also 13A18]

12J25

Archimedes值域[参见30G06, 32P05, 46S10, 47S10]

Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]

12J27

Krasner-Tate代数[主要见32P05; 参见46S10, 47S10]

Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]

12J99

其它

None of the above, but in this section

12Kxx

域的推广

Generalizations of fields

12K05

拟域[参见16Y30]

Near-fields [See also 16Y30]

12K10

半域[参见16Y60]

Semifields [See also 16Y60]

12K99

其它

None of the above, but in this section

12Lxx

与逻辑的联系

Connections with logic

12L05

可判定性[参见03B25]

Decidability [See also 03B25]

12L10

超积[参见03C20]

Ultraproducts [See also 03C20]

12L12

模型论[参见03C60]

Model theory [See also 03C60]

12L15

非标准算术[参见03H15]

Nonstandard arithmetic [See also 03H15]

12L99

其它

None of the above, but in this section

12Yxx

域论和多项式的计算方面

Computational aspects of field theory and poly­nomials

12Y05

域论和多项式的计算方面

Computational aspects of field theory and polynomials

12Y99

其它

None of the above, but in this section

13-XX

交换代数

Commutative algebras

13-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

13-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

13-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

13-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

13-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

13-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

13Axx

一般交换环理论

General commutative ring theory

13A02

分次环[参见16W50]

Graded rings [See also 16W50]

13A05

整除性; 因式分解[参见13F15]

Divisibility; factorizations [See also 13F15]

13A15

理想; 乘法理想理论

Ideals; multiplicative ideal theory

13A18

赋值及其推广[参见12J20]

Valuations and their generalizations [See also 12J20]

13A30

理想的结合分次环(Rees, 形式环), 解析扩展和有关论题

Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics

13A35

特征p方法(Frobenius自同态)与特征p约化; 胎紧闭包[参见13B22]

Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]

13A50

交换环上群的作用; 不变量理论[参见14L24]

Actions of groups on commutative rings; invariant theory [See also 14L24]

13A99

其它

None of the above, but in this section

13Bxx

环扩张及相关课题

Ring extensions and related topics

13B02

扩张理论

Extension theory

13B05

Galois理论

Galois theory

13B10

态射

Morphisms

13B21

整相关; 上升, 下降

Integral dependence; going up, going down

13B22

环和理想的整闭包[参见13A35]; 整闭环, 相关环(日本的等)

Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)

13B25

交换环上的多项式[参见11C08, 11T06, 13F20, 13M10]

Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]

13B30

分式环与局部化[参见16S85]

Rings of fractions and localization [See also 16S85]

13B35

完备化[参见13J10]

Completion [See also 13J10]

13B40

Étale和平坦扩张; Hensel; Artin逼近[参见13J15, 14B12, 14B25]

Étale and flat extensions; Henselization; Artin approxi­mation [See also 13J15, 14B12, 14B25]

13B99

其它

None of the above, but in this section

13Cxx

模和理想理论

Theory of modules and ideals

13C05

结构, 分类定理

Structure, classification theorems

13C10

射影与自由模以及理想[参见19A13]

Projective and free modules and ideals [See also 19A13]

13C11

内射与平坦模以及理想

Injective and flat modules and ideals

13C12

挠模与理想

Torsion modules and ideals

13C13

其它特殊类型

Other special types

13C14

Cohen-Macaulay[参见13H10]

Cohen-Macaulay modules [See also 13H10]

13C15

维数理论, 深度, 相关环(悬链线等)

Dimension theory, depth, related rings (catenary, etc.)

13C20

类群[参见11R29]

Class groups [See also 11R29]

13C40

环绕, 完全相交与行列式理想[参见14M06, 14M10, 14M12]

Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]

13C60

模范畴

Module categories

13C99

其它

None of the above, but in this section

13Dxx

()同调方法(非交换环, 16Exx; 一般范畴, 18Gxx)

Homological methods (For noncommutative rings, see 16Exx; for general categories, see 18Gxx)

13D02

合冲与预解, 复合

Syzygies and resolutions, complexes

13D03

交换环与交换代数的()同调(: HochschildAndré-Quillen、循环、二面体等)

(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)

13D05

()同调维数

Homological dimension

13D07

模上的同调函子(TorExt)

Homological functors on modules (Tor, Ext, etc.)

13D09

导出范畴

Derived categories

13D10

变形和无穷小方法[参见14B10, 14B12, 14D15, 32Gxx]

Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]

13D15

Grothendieck, K-理论[参见14C35, 18F30, 19Axx, 19D50]

Grothendieck groups, K-theory [See also 14C35, 18F30, 19Axx, 19D50]

13D22

同调猜想(相交定理)

Homological conjectures (intersection theorems)

13D30

挠理论[参见13C12, 18E40]

Torsion theory [See also 13C12, 18E40]

13D40

Hilbert-Samuel函数和Hilbert-Kunz函数; Poincaré级数

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series

13D45

局部上同调[参见14B15]

Local cohomology [See also 14B15]

13D99

其它

None of the above, but in this section

13Exx

链条件, 有限性条件

Chain conditions, finiteness conditions

13E05

Noether环与模

Noetherian rings and modules

13E10

Artin环与模, 有限维代数

Artinian rings and modules, finite-dimensional algebras

13E15

有限生成或表示的环与模; 生成元的数

Rings and modules of finite generation or presentation; number of generators

13E99

其它

None of the above, but in this section

13Fxx

算术环与其它特殊环

Arithmetic rings and other special rings

13F05

Dedekind, Prüfer, Krull环和Mori环及其推广

Dedekind, Prüfer, Krull and Mori rings and their generalizations

13F07

Euclid环及其推广

Euclidean rings and generalizations

13F10

主理想环

Principal ideal rings

13F15

由因式分解性质定义的环(例如: 原子, 阶乘, 半阶乘)[参见13A05, 14M05]

Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]

13F20

多项式环和理想; 整数值多项式的环[参见11C08, 13B25]

Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

13F25

形式幂级数环[参见13J05]

Formal power series rings [See also 13J05]

13F30

赋值环[参见13A18]

Valuation rings [See also 13A18]

13F35

Witt向量及相关环

Witt vectors and related rings

13F40

优环

Excellent rings

13F45

半正规环

Seminormal rings

13F50

直化律环, Hodge代数

Rings with straightening laws, Hodge algebras

13F55

Stanley-Reisner面环; 单纯复形[参见55U10]

Stanley-Reisner face rings; simplicial complexes [See also 55U10]

13F60

聚类代数

Cluster algebras

13F99

其它

None of the above, but in this section

13Gxx

整体域

Integral domains

13G05

整体域

Integral domains

13G99

其它

None of the above, but in this section

13Hxx

局部环和半局部环

Local rings and semilocal rings

13H05

正则局部环

Regular local rings

13H10

特殊类型(Cohen-MacaulayGorensteinBuchsbaum)[参见14M05]

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

13H15

乘法理论与相关课题[参见14C17]

Multiplicity theory and related topics [See also 14C17]

13H99

其它

None of the above, but in this section

13Jxx

拓扑环和模[参见16W60, 16W80]

Topological rings and modules [See also 16W60, 16W80]

13J05

幂级数环[参见13F25]

Power series rings [See also 13F25]

13J07

解析代数和解析环[参见32B05]

Analytical algebras and rings [See also 32B05]

13J10

完备环, 完备化[参见13B35]

Complete rings, completion [See also 13B35]

13J15

Hensel[参见13B40]

Henselian rings [See also 13B40]

13J20

整体拓扑环

Global topological rings

13J25

有序环[参见06F25]

Ordered rings [See also 06F25]

13J30

实代数[参见12D15, 14Pxx]

Real algebra [See also 12D15, 14Pxx]

13J99

其它

None of the above, but in this section

13Lxx

逻辑应用于交换代数[参见03Cxx, 03Hxx]

Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]

13L05

逻辑应用于交换代数[参见03Cxx, 03Hxx]

Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]

13L99

其它

None of the above, but in this section

13Mxx

有限交换环(数论方面, 11Txx)

Finite commutative rings (For number-theoretic aspects, see 11Txx)

13M05

结构

Structure

13M10

多项式

Polynomials

13M99

其它

None of the above, but in this section

13Nxx

微分代数[参见12H05, 14F10]

Differential algebra [See also 12H05, 14F10]

13N05

微分模

Modules of differentials

13N10

微分算子环及其模[参见16S32, 32C38]

Rings of differential operators and their modules [See also 16S32, 32C38]

13N15

求导

Derivations

13N99

其它

None of the above, but in this section

13Pxx

计算方面和应用[参见14Qxx, 68W30]

Computational aspects and applications [See also 14Qxx, 68W30]

13P05

多项式, 因式分解[参见12Y05]

Polynomials, factorization [See also 12Y05]

13P10

Gröbner; 理想和模的其它基(例如: Janet基和边界基)

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)

13P15

解多项式系统; 结式

Solving polynomial systems; resultants

13P20

计算同调代数[参见13Dxx]

Computational homological algebra [See also 13Dxx]

13P25

交换代数的应用(例如: 统计学、控制理论、最优化等)

Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)

13P99

其它

None of the above, but in this section

14-XX

代数几何

Algebraic geometry

14-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

14-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

14-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

14-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

14-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

14-05

会议录、会议、文集等

Proceedings, conferences, collections, etc.

14Axx

基础

Foundations

14A05

相关交换代数[参见13-XX]

Relevant commutative algebra [See also 13-XX]

14A10

簇和态射

Varieties and morphisms

14A15

概型和态射

Schemes and morphisms

14A20

推广(代数空间, 叠加)

Generalizations (algebraic spaces, stacks)

14A22

非交换代数几何[参见16S38]

Noncommutative algebraic geometry [See also 16S38]

14A25

基本问题

Elementary questions

14A99

其它

None of the above, but in this section

14Bxx

局部理论

Local theory

14B05

奇异性[参见14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

14B07

奇异性的形变[参见14D15, 32S30]

Deformations of singularities [See also 14D15, 32S30]

14B10

无穷小方法[参见13D10]

Infinitesimal methods [See also 13D10]

14B12

局部形变理论、Artin逼近等[参见13B40, 13D10]

Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]

14B15

局部上同调[参见13D45, 32C36]

Local cohomology [See also 13D45, 32C36]

14B20

形式邻域

Formal neighborhoods

14B25

态射的局部结构: étale、平坦等[参见13B40]

Local structure of morphisms: étale, flat, etc. [See also 13B40]

14B99

其它

None of the above, but in this section

14Cxx

循环与子概型

Cycles and subschemes

14C05

参数化(ChowHilbert概型)

Parametrization (Chow and Hilbert schemes)

14C15

(等变的)Chow群和环; motives

(Equivariant) Chow groups and rings; motives

14C17

相交理论, 特征类, 相交重数[参见13H15]

Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]

14C20

除子, 线性系统, 可逆层

Divisors, linear systems, invertible sheaves

14C21

, , [参见53A60]

Pencils, nets, webs [See also 53A60]

14C22

Picard

Picard groups

14C25

代数闭链

Algebraic cycles

14C30

超越方法, Hodge理论[参见14D07, 32G20, 32J25, 32S35], Hodge猜想

Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture

14C34

Torelli问题[参见32G20]

Torelli problem [See also 32G20]

14C35

代数K-理论方法的应用[参见19Exx]

Applications of methods of algebraic K-theory [See also 19Exx]

14C40

Riemann-Roch定理[参见19E20, 19L10]

Riemann-Roch theorems [See also 19E20, 19L10]

14C99

其它

None of the above, but in this section

14Dxx

, 纤维化

Families, fibrations

14D05

族的结构(Picard-Lefschetz理论、单值[])

Structure of families (Picard-Lefschetz, monodromy, etc.)

14D06

纤维化, 退化

Fibrations, degenerations

14D07

Hodge结构的变分[参见32G20]

Variation of Hodge structures [See also 32G20]

14D10

算术基域(有限, 局部, 整体)

Arithmetic ground fields (finite, local, global)

14D15

形式方法; 形变[参见13D10, 14B07, 32Gxx]

Formal methods; deformations [See also 13D10, 14B07, 32Gxx]

14D20

代数模问题, 向量丛的模(解析模问题, 32G13)

Algebraic moduli problems, moduli of vector bundles (For analytic moduli problems, see 32G13)

14D21

数学物理中向量丛和模空间的应用(扭子理论, 瞬子, 量子场论)

Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)

14D22

细与粗模空间

Fine and coarse moduli spaces

14D23

叠加和模问题

Stacks and moduli problems

14D24

几何Langlands程序: 代数几何方面[参见22E57]

Geometric Langlands program: algebrogeometric aspects [See also 22E57]

14D99

其它

None of the above, but in this section

14Exx

双有理几何

Birational geometry

14E05

有理映射和双有理映射

Rational and birational maps

14E07

双有理自同构, Cremona群及推广

Birational automorphisms, Cremona group and genera­lizations

14E08

有理性问题[参见14M20]

Rationality questions [See also 14M20]

14E15

整体理论和奇异性分解[参见14B05, 32S20, 32S45]

Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]

14E16

McKay对应

McKay correspondence

14E18

弧与主积分法

Arcs and motivic integration

14E20

覆盖[参见14H30]

Coverings [See also 14H30]

14E22

分歧问题[参见11S15]

Ramification problems [See also 11S15]

14E25

嵌入

Embeddings

14E30

极小模型程序(Mori理论, 极值射线)

Minimal model program (Mori theory, extremal rays)

14E99

其它

None of the above, but in this section

14Fxx

()同调理论[参见13Dxx]

(Co)homology theory [See also 13Dxx]

14F05

, 层的导出范畴及相关构造[参见14H60, 14J60, 18F20, 32Lxx, 46M20]

Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

14F10

微分层和其它特殊层; D-modules; Bernstein-Sato理想及多项式[参见13Nxx, 32C38]

Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]

14F17

消没定理[参见32L20]

Vanishing theorems [See also 32L20]

14F18

乘法理想

Multiplier ideals

14F20

Étale与其它Grothendieck拓扑和上同调

Étale and other Grothendieck topologies and coho­mologies

14F22

概形的Brauer[参见12G05, 16K50]

Brauer groups of schemes [See also 12G05, 16K50]

14F25

经典实上同调和复上同调

Classical real and complex cohomology

14F30

p-进上同调, 结晶线上同调

p-adic cohomology, crystalline cohomology

14F35

同调论; 基本群[参见14H30]

Homotopy theory; fundamental groups [See also 14H30]

14F40

de Rham上同调[参见14C30, 32C35, 32L10]

de Rham cohomology [See also 14C30, 32C35, 32L10]

14F42

主上同调; 主同伦理论

Motivic cohomology; motivic homotopy theory

14F43

其它代数-几何()同调(例如: 相交、等变、LawsonDeligne()同调)

Other algebro-geometric (co)homologies (e.g., intersec­tion, equivariant, Lawson, Deligne (co)homologies)

14F45

拓扑性质

Topological properties

14F99

其它

None of the above, but in this section

14Gxx

算术问题, Diophantus几何[参见11Dxx, 11Gxx]

Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]

14G05

有理点

Rational points

14G10

ζ函数与相关问题[参见11G40](Birch-Swinnerton-Dyer猜想)

Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)

14G15

有限基域

Finite ground fields

14G17

正特征基域

Positive characteristic ground fields

14G20

局部基域

Local ground fields

14G22

刚性解析几何

Rigid analytic geometry

14G25

整体基域

Global ground fields

14G27

其它非代数闭基域

Other nonalgebraically closed ground fields

14G32

泛投射有限群(与模空间, 映射和模塔, Galois理论的关系)

Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)

14G35

模和Shimura[参见11F41, 11F46, 11G18]

Modular and Shimura varieties [See also 11F41, 11F46, 11G18]

14G40

算术簇和概型; Arakelov理论; 高度[参见11G50, 37P30]

Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]

14G50

应用于编码理论和密码学[参见94A60, 94B27, 94B40]

Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]

14G99

其它

None of the above, but in this section

14Hxx

曲线

Curves

14H05

代数函数; 函数域[参见11R58]

Algebraic functions; function fields [See also 11R58]

14H10

, (代数的)

Families, moduli (algebraic)

14H15

, (解析的)[参见30F10, 32Gxx]

Families, moduli (analytic) [See also 30F10, 32Gxx]

14H20

奇异性, 局部环[参见13Hxx, 14B05]

Singularities, local rings [See also 13Hxx, 14B05]

14H25

算术基域[参见11Dxx, 11G05, 14Gxx]

Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]

14H30

覆盖, 基本群[参见14E20, 14F35]

Coverings, fundamental group [See also 14E20, 14F35]

14H37

自同构

Automorphisms

14H40

Jacobi行列式, Prym[参见32G20]

Jacobians, Prym varieties [See also 32G20]

14H42

θ函数; Schottky问题[参见14K25, 32G20]

Theta functions; Schottky problem [See also 14K25, 32G20]

14H45

特殊曲线和低亏格曲线

Special curves and curves of low genus

14H50

平面和空间曲线

Plane and space curves

14H51

特殊除子(gonality, Brill-Noether理论)

Special divisors (gonality, Brill-Noether theory)

14H52

椭圆曲线[参见11G05, 11G07, 14Kxx]

Ellipse curve [See also 11G05, 11G07, 14Kxx]

14H55

Riemann曲面; Weierstrass; 间断序列[参见30Fxx]

Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]

14H57

Dessins d'enfants理论(算术方面, 11G32)

Dessins d'enfants theory (For arithmetic aspects, see 11G32)

14H60

曲线上的向量丛及其模[参见14D20, 14F05]

Vector bundles on curves and their moduli [See also 14D20, 14F05]

14H70

与可积系统的关系

Relationships with integrable systems

14H81

与物理的关系

Relationships with physics

14H99

其它

None of the above, but in this section

14Jxx

曲面与高维簇(解析理论, 32Jxx)

Surfaces and higher-dimensional varieties (For analytic theory, see 32Jxx)

14J10

, , 分类: 代数理论

Families, moduli, classification: algebraic theory

14J15

, 分类: 解析理论; 与模形式的关系[参见32G13]

Moduli, classification: analytic theory; relations with modular forms [See also 32G13]

14J17

奇异性[参见14B05, 14E15]

Singularities [See also 14B05, 14E15]

14J20

算术基域[参见11Dxx, 11G25, 11G35, 14Gxx]

Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]

14J25

特殊曲面(Hilbert模曲面, 14G35)

Special surfaces (For Hilbert modular surfaces, see 14G35)

14J26

有理曲面和直纹面

Rational and ruled surfaces

14J27

椭圆曲面

Elliptic surfaces

14J28

K3曲面和Enriques曲面

K3 surfaces and Enriques surfaces

14J29

一般型曲面

Surfaces of general type

14J30

3维簇[参见32Q25]

3-folds [See also 32Q25]

14J32

Calabi-Yau流形

Calabi-Yau manifolds

14J33

镜对称[参见11G42, 53D37]

Mirror symmetry [See also 11G42, 53D37]

14J35

4维簇

4-folds

14J40

n维簇(n >4)

n-folds (n >4)

14J45

Fano

Fano varieties

14J50

曲面的自同构和高维簇

Automorphisms of surfaces and higher-dimensional varieties

14J60

曲面上的向量丛和高维簇及其模[参见14D20, 14F05, 32Lxx]

Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]

14J70

超曲面

Hypersurfaces

14J80

曲面的拓扑(Donaldson多项式, Seiberg-Witten不变量)

Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)

14J81

与物理的关系

Relationships with physics

14J99

其它

None of the above, but in this section

14Kxx

Abel簇和概型

Abelian varieties and schemes

14K02

同种映射

Isogeny

14K05

代数理论

Algebraic theory

14K10

代数模, 分类[参见11G15]

Algebraic moduli, classification [See also 11G15]

14K12

子簇

Subvarieties

14K15

算术基域[参见11Dxx, 11Fxx, 11Gxx, 14Gxx]

Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx]

14K20

解析理论; Abel积分和微分

Analytic theory; abelian integrals and differentials

14K22

复数乘法[参见11G15]

Complex multiplication [See also 11G15]

14K25

θ函数[参见14H42]

Theta functions [See also 14H42]

14K30

Picard概型, 高阶Jacobi行列式[参见14H40, 32G20]

Picard schemes, higher Jacobians [See also 14H40, 32G20]

14K99

其它

None of the above, but in this section

14Lxx

代数群(线性代数群, 20Gxx; Lie代数, 17B45)

Algebraic Groups (For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45)

14L05

形式群, p-可除群[参见55N22]

Formal groups, p-divisible groups [See also 55N22]

14L10

群簇

Group varieties

14L15

群概型

Group schemes

14L17

仿射代数群, 超代数构造[参见17B45, 18D35]

Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]

14L24

几何不变量理论[参见13A50]

Geometric invariant theory [See also 13A50]

14L30

群作用于簇或概型()[参见13A50, 14L24]

Group actions on varieties or schemes (quotients) [See also 13A50, 14L24]

14L35

典型群(几何方面)[参见20Gxx, 51N30]

Classical groups (geometric aspects) [See also 20Gxx, 51N30]

14L40

其它代数群(几何方面)

Other algebraic groups (geometric aspects)

14L99

其它

None of the above, but in this section

14Mxx

特殊簇

Special varieties

14M05

由环条件(阶乘, Cohen-Macaulay, 半正规)定义的簇[参见13F45, 13H10]

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F45, 13H10]

14M06

环绕[参见13C40]

Linkage [See also 13C40]

14M07

低余维问题

Low codimension problems

14M10

完全相交[参见13C40]

Complete intersections [See also 13C40]

14M12

行列式簇[参见13C40]

Determinantal varieties [See also 13C40]

14M15

Grassmann, Schubert, 旗流形[参见32M10, 51M35]

Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

14M17

齐次空间及其推广[参见32M10, 53C30, 57T15]

Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]

14M20

有理和单有理簇[参见14E08]

Rational and unirational varieties [See also 14E08]

14M22

有理连通簇

Rationally connected varieties

14M25

环面簇, Newton多面体[参见52B20]

Toric varieties, Newton polyhedra [See also 52B20]

14M27

紧化; 对称与球形簇

Compactifications; symmetric and spherical varieties

14M30

超簇[参见32C11, 58A50]

Supervarieties [See also 32C11, 58A50]

14M99

其它

None of the above, but in this section

14Nxx

射影几何和枚举几何[参见51-XX]

Projective and enumerative geometry [See also 51-XX]

14N05

射影技巧[参见51N35]

Projective techniques [See also 51N35]

14N10

枚举问题(组合问题)

Enumerative problems (combinatorial problems)

14N15

经典问题, Schubert演算

Classical problems, Schubert calculus

14N20

线性子空间的构形和布局

Configurations and arrangements of linear subspaces

14N25

低度簇

Varieties of low degree

14N30

相伴问题

Adjunction problems

14N35

Gromov-Witten不变量, 量子上同调, Gopakumar-Vafa不变量, Donaldson-Thomas不变量[参见53D45]

Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

14N99

其它

None of the above, but in this section

14Pxx

实代数和实解析几何

Real algebraic and real analytic geometry

14P05

实代数集[参见12D15, 13J30]

Real algebraic sets [See also 12D15, 13J30]

14P10

半代数集和相关空间

Semialgebraic sets and related spaces

14P15

实解析集和半解析集[参见32B20, 32C05]

Real analytic and semianalytic sets [See also 32B20, 32C05]

14P20

Nash函数和流形[参见32C07, 58A07]

Nash functions and manifolds [See also 32C07, 58A07]

14P25

实代数簇的拓扑

Topology of real algebraic varieties

14P99

其它

None of the above, but in this section

14Qxx

代数几何的计算方面[参见12Y05, 13Pxx, 68W30]

Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]

14Q05

曲线

Curves

14Q10

曲面, 超曲面

Surfaces, hypersurfaces

14Q15

高维簇

Higher-dimensional varieties

14Q20

有效性, 复杂性

Effectivity, complexity

14Q99

其它

None of the above, but in this section

14Rxx

仿射几何

Affine geometry

14R05

仿射簇的分类

Classification of affine varieties

14R10

仿射空间(自同构, 嵌入, 异种结构, 消没问题)

Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)

14R15

Jacobi问题

Jacobian problem

14R20

在仿射簇上的群作用[参见13A50, 14L30]

Group actions on affine varieties [See also 13A50, 14L30]

14R25

仿射纤维化[参见14D06]

Affine fibrations [See also 14D06]

14R99

其它

None of the above, but in this section

14Txx

Tropical几何[参见12K10, 14M25, 14N10, 52B20]

Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]

14T05

Tropical几何[参见12K10, 14M25, 14N10, 52B20]

Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]

14T99

其它

None of the above, but in this section

15-XX

线性代数和多重线性代数; 矩阵论

Linear and multilinear algebra; matrix theory

15-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

15-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

15-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

15-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

15-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

15-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

15Axx

基础线性代数

Basic linear algebra

15A03

向量空间, 线性相关,

Vector spaces, linear dependence, rank

15A04

线性变换, 半线性变换

Linear transformations, semilinear transformations

15A06

线性方程

Linear equations

15A09

矩阵反演, 广义逆

Matrix inversion, generalized inverses

15A12

矩阵的条件[参见65F35]

Conditioning of matrices [See also 65F35]

15A15

行列式, 积和式, 其它特殊的矩阵函数[参见19B10, 19B14]

Determinants, permanents, other special matrix functions [See also 19B10, 19B14]

15A16

矩阵指数与矩阵相似函数

Matrix exponential and similar functions of matrices

15A18

特征值, 奇异值和特征向量

Eigenvalues, singular values, and eigenvectors

15A21

标准型, 约化, 分类

Canonical forms, reductions, classification

15A22

矩阵束[参见47A56]

Matrix pencils [See also 47A56]

15A23

矩阵的因式分解

Factorization of matrices

15A24

矩阵方程和恒等式

Matrix equations and identities

15A27

交换性

Commutativity

15A29

逆问题

Inverse problems

15A30

矩阵的代数系统[参见16S50, 20Gxx, 20Hxx]

Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]

15A33

特殊环上的矩阵(四元数、有限域等)

Matrices over special rings (quaternions, finite fields, etc.)

15A39

线性不等式

Linear inequalities

15A42

涉及特征值和特征向量的不等式

Inequalities involving eigenvalues and eigenvectors

15A45

各种涉及矩阵的不等式

Miscellaneous inequalities involving matrices

15A54

一个或多个变量函数环上的矩阵

Matrices over function rings in one or more variables

15A60

矩阵的范数, 数值范围, 泛函分析在矩阵论中的应用[参见65F35, 65J05]

Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]

15A63

二次型和双线性型, 内积[主要见11Exx]

Quadratic and bilinear forms, inner products [See mainly 11Exx]

15A66

Clifford代数, 旋量

Clifford algebras, spinors

15A69

多重线性代数, 张量积

Multilinear algebra, tensor products

15A72

向量和张量代数, 不变量理论[参见13A50, 14L24]

Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]

15A75

外代数, Grassmann代数

Exterior algebra, Grassmann algebras

15A78

用模构建的其它代数

Other algebras built from modules

15A80

最大加与相关代数

Max-plus and related algebras

15A83

矩阵完备化问题

Matrix completion problems

15A86

线性保持问题

Linear preserver problems

15A99

杂题

Miscellaneous topics

15Bxx

特殊矩阵

Special matrices

15B05

Toeplitz, Cauchy及其相关矩阵

Toeplitz, Cauchy, and related matrices

15B10

正交矩阵

Orthogonal matrices

15B15

模糊矩阵

Fuzzy matrices

15B33

特殊环上的矩阵(四元数、有限域等)

Matrices over special rings (quaternions, finite fields, etc.)

15B34

BooleHadamard矩阵

Boolean and Hadamard matrices

15B35

符号模式矩阵

Sign pattern matrices

15B36

整数矩阵[参见11C20]

Matrices of integers [See also 11C20]

15B48

正矩阵及其推广; 矩阵锥

Positive matrices and their generalizations; cones of matrices

15B51

随机矩阵

Stochastic matrices

15B52

随机矩阵

Random matrices

15B57

Hermitian, -Hermitian及其相关矩阵

Hermitian, skew-Hermitian, and related matrices

15B99

其它

None of the above, but in this section

16-XX

结合环与结合代数(交换情形, 13-XX)

Associative rings and algebras (For the commutative case, see 13-XX)

16-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

16-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

16-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

16-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

16-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

16-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

16Bxx

一般问题与杂题

General and miscellaneous

16B50

范畴论的方法和结果(16D90除外)[参见18-XX]

Category-theoretic methods and results (except as in 16D90) [See also 18-XX]

16B70

逻辑应用[参见03Cxx]

Applications of logic [See also 03Cxx]

16B99

其它

None of the above, but in this section

16Dxx

, 双模和理想

Modules, bimodules and ideals

16D10

一般模理论

General module theory

16D20

双模

Bimodules

16D25

理想

Ideals

16D30

无穷维单环(16Kxx除外)

Infinite-dimensional simple rings (except as in 16Kxx)

16D40

自由模, 射影模和平坦模及理想[参见19A13]

Free, projective, and flat modules and ideals [See also 19A13]

16D50

内射模, 自内射环[参见16L60]

Injective modules, self-injective rings [See also 16L60]

16D60

单模和半单模, 本原环和理想

Simple and semisimple modules, primitive rings and ideals

16D70

结构和分类(16Gxx除外), 直和分解, 消去

Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation

16D80

模和理想的其它类[参见16G50]

Other classes of modules and ideals [See also 16G50]

16D90

模范畴[参见16Gxx, 16S90]; 范畴论中的模理论; Morita等价与对偶

Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality

16D99

其它

None of the above, but in this section

16Exx

同调方法(交换环, 13Dxx; 一般范畴, 18Gxx)

Homological methods (For commutative rings, see 13Dxx; for general categories, see 18Gxx)

16E05

合冲, 预解, 复形

Syzygies, resolutions, complexes

16E10

同调维数

Homological dimension

16E20

Grothendieck群、K-理论等[参见18F30, 19Axx, 19D50]

Grothendieck groups, K-theory, etc. [See also 18F30, 19Axx, 19D50]

16E30

模上的同调函子(TorExt)

Homological functors on modules (Tor, Ext, etc.)

16E35

导出范畴

Derived categories

16E40

环和代数的()同调(例如: Hochschild、循环、二面体等)

(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)

16E45

微分分次代数及其应用

Differential graded algebras and applications

16E50

von Neumann正则环及其推广

von Neumann regular rings and generalizations

16E60

半遗传环和遗传环、自由理想环、Sylvester环等

Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.

16E65

环上的同调条件(正则、GorensteinCohen-Macaulay等环的推广)

Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)

16E99

其它

None of the above, but in this section

16Gxx

环和代数的表示理论

Representation theory of rings and algebras

16G10

Artin环的表示

Representations of Artinian rings

16G20

箭图和偏序集的表示

Representations of quivers and partially ordered sets

16G30

交换环上的整环, 格和代数的表示[参见16Hxx]

Representations of orders, lattices, algebras over commutative rings [See also 16Hxx]

16G50

Cohen-Macaulay

Cohen-Macaulay modules

16G60

表示类型(有限、驯顺、非驯顺等)

Representation type (finite, tame, wild, etc.)

16G70

Auslander-Reiten序列(几乎分裂序列)Auslander-Reiten箭图

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

16G99

其它

None of the above, but in this section

16Hxx

代数与整环(算术方面, 11R52, 11R54, 11S45;表示理论, 16G30)

Algebras and orders (For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30)

16H05

可分代数(例如: 四元数代数、Azumaya代数等)

Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)

16H10

可分代数的整环

Orders in separable algebras

16H15

交换整环

Commutative orders

16H20

整环上的格

Lattices over orders

16H99

其它

None of the above, but in this section

16Kxx

除环与半单Artin[参见12E15, 15A30]

Division rings and semisimple Artin rings [See also 12E15, 15A30]

16K20

有限维的(叉积, 16S35)

Finite-dimensional (For crossed products, see 16S35)

16K40

无限维的与一般情形

Infinite-dimensional and general

16K50

Brauer[参见12G05, 14F22]

Brauer groups [See also 12G05, 14F22]

16K99

其它

None of the above, but in this section

16Lxx

局部环及其推广

Local rings and generalizations

16L30

非交换局部环和半局部环, 完美环

Noncommutative local and semilocal rings, perfect rings

16L60

Frobenius[参见16D50]

Quasi-Frobenius rings [See also 16D50]

16L99

其它

None of the above, but in this section

16Nxx

环的根和根性质

Radicals and radical properties of rings

16N20

Jacobson, 拟乘法

Jacobson radical, quasimultiplication

16N40

零和幂零根, 集合, 理想与环

Nil and nilpotent radicals, sets, ideals, rings

16N60

素环与半素环[参见16D60, 16U10]

Prime and semiprime rings [See also 16D60, 16U10]

16N80

广义根和环(模范畴中的根, 16S90)

General radicals and rings (For radicals in module categories, see 16S90)

16N99

其它

None of the above, but in this section

16Pxx

链条件, 增长条件和其它有限性形式

Chain conditions, growth conditions, and other forms of finiteness

16P10

有限环和有限维代数(半单情形, 16K20; 交换情形, 11Txx, 13Mxx)

Finite rings and finite-dimensional algebras (For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx)

16P20

Artin环和模

Artinian rings and modules

16P40

Noether环和模

Noetherian rings and modules

16P50

局部化与Noether[参见16U20]

Localization and Noetherian rings [See also 16U20]

16P60

零化子与直和项上的链条件: Goldie型条件[参见16U20], Krull

Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension

16P70

其它子模、理想、子环等上的链条件; 凝聚

Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence

16P90

增长率, Gelfand-Kirillov维数

Growth rate, Gelfand-Kirillov dimension

16P99

其它

None of the above, but in this section

16Rxx

具有多项式恒等式的环

Rings with polynomial identity

16R10

T理想, 恒等式, 环与代数的簇

T-ideals, identities, varieties of rings and algebras

16R20

半素多项式恒等式环, 交换环上矩阵中的环可嵌入

Semiprime p.i. rings, rings embeddable in matrices over commutative rings

16R30

迹环与不变量理论

Trace rings and invariant theory

16R40

交换环上矩阵恒等式以外的恒等式

Identities other than those of matrices over commutative rings

16R50

其它恒等式(广义多项式, 有理的, 对合)

Other kinds of identities (generalized polynomial, rational, involution)

16R60

泛函恒等式

Functional identities

16R99

其它

None of the above, but in this section

16Sxx

各种构造下的环与代数

Rings and algebras arising under various constructions

16S10

由泛性质确定的环(自由代数、余积、逆的附加等)

Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)

16S15

有限生成, 有限表示, 范式(菱形引理, 项重写)

Finite generation, finite representability, normal forms (diamond lemma, term-rewriting)

16S20

中心化与正规扩张

Centralizing and normalizing extensions

16S30

Lie代数的泛包络代数[主要见17B35]

Universal enveloping algebras of Lie algebras [See mainly 17B35]

16S32

微分算子环[参见13N10, 32C38]

Rings of differential operators [See also 13N10, 32C38]

16S34

群环[参见20C05, 20C07], Laurent多项式环

Group rings [See also 20C05, 20C07], Laurent polynomial rings

16S35

挠群环和斜群环, 叉积

Twisted and skew group rings, crossed products

16S36

普通多项式环和斜多项式环以及半群环[参见20M25]

Ordinary and skew polynomial rings and semigroup rings [See also 20M25]

16S37

二次和Koszul代数

Quadratic and Koszul algebras

16S38

来自非交换代数几何的环[参见14A22]

Rings arising from non-commutative algebraic geometry [See also 14A22]

16S40

一般Hopf作用的Smash[参见16T05]

Smash products of general Hopf actions [See also 16T05]

16S50

自同态环; 矩阵环[参见15-XX]

Endomorphism rings; matrix rings [See also 15-XX]

16S60

函数环, 子直积, 环层

Rings of functions, subdirect products, sheaves of rings

16S70

用理想表示的环扩张

Extensions of rings by ideals

16S80

环形变[参见13D10, 14D15]

Deformations of rings [See also 13D10, 14D15]

16S85

分式环与局部化[参见13B30]

Rings of fractions and localizations [See also 13B30]

16S90

挠理论; 模范畴上的根[参见13D30, 18E40](环的根, 16Nxx)

Torsion theories; radicals on module categories [See also 13D30, 18E40](For radicals of rings, see 16Nxx)

16S99

其它

None of the above, but in this section

16Txx

Hopf代数, 量子群及相关课题

Hopf algebras, quantum groups and related topics

16T05

Hopf代数及其应用[参见16S40, 57T05]

Hopf algebras and their applications [See also 16S40, 57T05]

16T10

双代数

Bialgebras

16T15

余代数与余模;余环

Coalgebras and comodules; corings

16T20

量子群的环论方面[参见17B37, 20G42, 81R50]

Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]

16T25

Yang-Baxter方程

Yang-Baxter equations

16T30

与组合学的联系

Connections with combinatorics

16T99

其它

None of the above, but in this section

16Uxx

元素的条件

Conditions on elements

16U10

整环

Integral domains

16U20

Ore, 乘性集, Ore局部化

Ore rings, multiplicative sets, Ore localization

16U30

可除性, 非交换惟一因式分解整环

Divisibility, noncommutative UFDs

16U60

单位, 单位群

Units, groups of units

16U70

中心, 正规化子(不变元)

Center, normalizer (invariant elements)

16U80

交换性的推广

Generalizations of commutativity

16U99

其它

None of the above, but in this section

16Wxx

具有附加结构的环和代数

Rings and algebras with additional structure

16W10

具有对合的环; Lie结构, Jordan结构和其它非结合结构[参见17B60, 17C50, 46Kxx]

Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]

16W20

自同构与自同态

Automorphisms and endomorphisms

16W22

群和半群的作用; 不变量理论

Actions of groups and semigroups; invariant theory

16W25

求导, Lie代数的作用

Derivations, actions of Lie algebras

16W50

分次环与分次模

Graded rings and modules

16W55

超”(或“斜”)结构[参见17A70, 17Bxx, 17C70](外代数, 15A75; Clifford代数, 11E88, 15A66)

Super” (or “skew”) structure [See also 17A70, 17Bxx, 17C70] (For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66)

16W60

赋值, 完备性, 形式幂级数和相关构造[参见13Jxx]

Valuations, completions, formal power series and related constructions [See also 13Jxx]

16W70

滤子化环; 过滤和分次技巧

Filtered rings; filtrational and graded techniques

16W80

拓扑环和有序环及模[参见06F25, 13Jxx]

Topological and ordered rings and modules [See also 06F25, 13Jxx]

16W99

其它

None of the above, but in this section

16Yxx

推广(非结合环, 17-XX)

Generalizations (For nonassociative rings, see 17-XX)

16Y30

拟环[参见12K05]

Near-rings [See also 12K05]

16Y60

半环[参见12K10]

Semirings [See also 12K10]

16Y99

其它

None of the above, but in this section

16Zxx

结合环的计算方面

Computational aspects of associative rings

16Z05

结合环的计算方面[参见68W30]

Computations aspects of associative rings [See also 68W30]

16Z99

其它

None of the above, but in this section

17-XX

非结合环与非结合代数

Nonassociative rings and algebras

17-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

17-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

17-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

17-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

17-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

17-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

17-08

计算方法

Computational methods

17Axx

一般非结合环

General nonassociative rings

17A01

一般理论

General theory

17A05

幂结合环

Power-associative rings

17A15

非交换Jordan代数

Noncommutative Jordan algebras

17A20

可拐代数

Flexible algebras

17A30

满足其它恒等式的代数

Algebras satisfying other identities

17A32

Leibniz代数

Leibniz algebras

17A35

可除代数

Division algebras

17A36

自同构, 求导, 其它算子

Automorphisms, derivations, other operators

17A40

三元合成

Ternary compositions

17A42

其它n元合成(n≥3)

Other n-ary compositions (n≥3)

17A45

二次代数(非二次Jordan代数)

Quadratic algebras (but not quadratic Jordan algebras)

17A50

自由代数

Free algebras

17A60

结构理论

Structure theory

17A65

根理论

Radical theory

17A70

超代数

Superalgebras

17A75

合成代数

Composition algebras

17A80

赋值代数

Valued algebras

17A99

其它

None of the above, but in this section

17Bxx

Lie代数和Lie超代数(Lie, 22Exx)

Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)

17B01

恒等式, 自由Lie()代数

Identities, free Lie (super) algebras

17B05

结构理论

Structure theory

17B08

余伴随轨道; 幂零簇

Coadjoint orbits; nilpotent varieties

17B10

表示, 代数理论()

Representations, algebraic theory (weights)

17B15

表示, 解析理论

Representations, analytic theory

17B20

, 半单, 约化()代数

Simple, semisimple, reductive (super) algebras

17B22

根系

Root systems

17B25

例外()代数

Exceptional (super)algebras

17B30

可解代数, 幂零()代数

Solvable, nilpotent (super) algebras

17B35

泛包络()代数[参见16S30]

Universal enveloping (super) algebras [See also 16S30]

17B37

量子群(量子包络代数)和有关形变[参见16T20, 20G42, 81R50, 82B23]

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

17B40

自同构, 求导, 其它算子

Automorphisms, derivations, other operators

17B45

线性代数群的Lie代数[参见14Lxx20Gxx]

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]

17B50

Lie()代数

Modular Lie (super) algebras

17B55

Lie()代数中的同调方法

Homological methods in Lie (super)algebras

17B56

Lie()代数的上同调

Cohomology of Lie (super) algebras

17B60

伴有其它结构(结合的、Jordan)Lie()代数[参见16W10, 17C40, 17C50]

Lie (super) algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]

17B62

Lie双代数; Lie余代数

Lie bialgebras; Lie coalgebras

17B63

Poisson代数

Poisson algebras

17B65

无限维Lie()代数[参见22E65]

Infinite-dimensional Lie (super) algebras [See also 22E65]

17B66

向量域Lie()代数与有关的()代数

Lie algebras of vector fields and related (super) algebras

17B67

Kac-Moody()代数; 扩展的仿射Lie代数; 环形Lie代数

Kac-Moody (super) algebras; extended affine Lie algebras; toroidal Lie algebras

17B68

Virasoro代数和相关代数

Virasoro and related algebras

17B69

极点算子; 极点算子代数和相关结构

Vertex operators; vertex operator algebras and related structures

17B70

分次Lie()代数

Graded Lie (super) algebras

17B75

着色Lie()代数

Color Lie (super) algebras

17B80

应用于可积系统

Applications to integrable systems

17B81

应用于物理

Applications to physics

17B99

其它

None of the above, but in this section

17Cxx

Jordan代数(代数, 三元组和对)

Jordan algebras (algebras, triples and pairs)

17C05

恒等式与自由Jordan结构

Identities and free Jordan structures

17C10

结构理论

Structure theory

17C17

Radicals

17C20

, 半单代数

Simple, semisimple algebras

17C27

幂等的, Peirce分解

Idempotents, Peirce decompositions

17C30

结合群, 自同构

Associated groups, automorphisms

17C36

结合流形

Associated manifolds

17C37

结合几何

Associated geometries

17C40

例外Jordan结构

Exceptional Jordan structures

17C50

具有其它结构的Jordan结构[参见16W10]

Jordan structures associated with other structures [See also 16W10]

17C55

有限维结构

Finite-dimensional structures

17C60

可除代数

Division algebras

17C65

Banach空间和代数上的Jordan结构[参见46H70, 46L70]

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]

17C70

超结构

Super structures

17C90

应用于物理

Applications to physics

17C99

其它

None of the above, but in this section

17Dxx

其它非结合环与代数

Other nonassociative rings and algebras

17D05

交错环

Alternative rings

17D10

Mal'cev(Mal'tsev)环与代数

Mal'cev (Mal'tsev) rings and algebras

17D15

右交错环

Right alternative rings

17D20

(γ, δ)-, 包含(1, 1)-

(γ, δ)-rings, including (1, 1)-rings

17D25

Lie容许代数

Lie-admissible algebras

17D92

遗传代数

Genetic algebras

17D99

其它

None of the above, but in this section

18-XX

范畴论; 同调代数(交换环, 13Dxx;结合环16Exx, 20Jxx, 拓扑群和相关结构57Txx; 代数拓扑, 参见55Nxx55Uxx)

Category theory; homological algebra (For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx see also 55Nxx and 55Uxx for algebraic topology)

18-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

18-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

18-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

18-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

18-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

18-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

18Axx

范畴与函子的一般理论

General theory of categories and functors

18A05

定义与推广

Definitions, generalizations

18A10

, 图解概型, 预范畴[特别见20L05]

Graphs, diagram schemes, precategories [See especially 20L05]

18A15

基础, 与逻辑和演绎系统的关系[参见03-XX]

Foundations, relations to logic and deductive systems [See also 03-XX]

18A20

满射, 单射, 特殊类射, 零射

Epimorphisms, monomorphisms, special classes of morphisms, null morphisms

18A22

函子的特性(忠实的、满的等)

Special properties of functors (faithful, full, etc.)

18A23

自然射, 双自然射

Natural morphisms, dinatural morphisms

18A25

函子范畴, 逗号范畴

Functor categories, comma categories

18A30

极限与上极限(积、和、有向极限、前推、纤维积、等化子、核、端和上端等)

Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)

18A32

射的因子分解, 子结构, 商结构, 同余, 融和

Factorization of morphisms, substructures, quotient structures, congruences, amalgams

18A35

容许极限范畴(完全范畴), 保极限函子, 完备化

Categories admitting limits (complete categories), functors preserving limits, completions

18A40

伴随函子(泛构造、反射子范畴、Kan扩张等)

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)

18A99

其它

None of the above, but in this section

18Bxx

特殊范畴

Special categories

18B05

集范畴, 特征[参见03-XX]

Category of sets, characterizations [See also 03-XX]

18B10

关系范畴, 加法关系

Category of relations, additive relations

18B15

嵌入定理, 泛范畴[参见18E20]

Embedding theorems, universal categories [See also 18E20]

18B20

机器范畴, 自动机, 运算范畴[参见03D05, 68Qxx]

Categories of machines, automata, operative categories [See also 03D05, 68Qxx]

18B25

普通概念[参见03G30]

Topoi [See also 03G30]

18B30

拓扑空间的范畴与连续映射[参见54-XX]

Categories of topological spaces and continuous mappings [See also 54-XX]

18B35

前序, 序和格(被视作范畴)[参见06-XX]

Preorders, orders and lattices (viewed as categories) [See also 06-XX]

18B40

广群, 半广群, 半群, (被视作范畴)[参见20Axx, 20L05, 20Mxx]

Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]

18B99

其它

None of the above, but in this section

18Cxx

范畴与理论

Categories and theories

18C05

等价范畴[参见03C05, 08C05]

Equational categories [See also 03C05, 08C05]

18C10

理论(例如: 代数理论), 结构和语义学[参见03G30]

Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]

18C15

三元组(=标准构造, 一元或三元组), 三元组代数, 同调与三元组导出函子[参见18Gxx]

Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]

18C20

与一元组相伴的代数和Kleisli范畴

Algebras and Kleisli categories associated with monads

18C30

梗概及其推广

Sketches and generalizations

18C35

可达和局部有规矩范畴

Accessible and locally presentable categories

18C50

形式语言的范畴语义学[参见68Q55, 68Q65]

Categorical semantics of formal languages [See also 68Q55, 68Q65]

18C99

其它

None of the above, but in this section

18Dxx

有结构的范畴

Categories with structure

18D05

双重范畴, 2范畴, 双范畴及其推广

Double categories, 2-categories, bicategories and generalizations

18D10

单项范畴(=乘法范畴), 对称单项范畴, 辫范畴[参见19D23]

Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]

18D15

闭范畴(闭单项范畴和Descartes闭范畴等)

Closed categories (closed monoidal and Cartesian closed categories, etc.)

18D20

浓缩范畴(闭范畴或单项范畴之上)

Enriched categories (over closed or monoidal categories)

18D25

强函子, 强附加

Strong functors, strong adjunctions

18D30

纤维范畴

Fibered categories

18D35

范畴中的结构化对象(群对象等)

Structured objects in a category (group objects, etc.)

18D50

Operads[参见55P48]

Operads [See also 55P48]

18D99

其它

None of the above, but in this section

18Exx

Abel范畴

Abelian categories

18E05

预加性范畴, 加法范畴

Preadditive, additive categories

18E10

正合范畴, Abel范畴

Exact categories, abelian categories

18E15

Grothendieck范畴

Grothendieck categories

18E20

嵌入定理[参见18B15]

Embedding theorems [See also 18B15]

18E25

导出函子和卫星

Derived functors and satellites

18E30

导出范畴, 三角范畴

Derived categories, triangulated categories

18E35

范畴的局部化

Localization of categories

18E40

挠理论, [参见13D30, 16S90]

Torsion theories, radicals [See also 13D30, 16S90]

18E99

其它

None of the above, but in this section

18Fxx

范畴与几何

Categories and geometry

18F05

局部范畴与函子

Local categories and functors

18F10

Grothendieck拓扑[参见14F20]

Grothendieck topologies [See also 14F20]

18F15

抽象流形与纤维丛[参见55Rxx, 57Pxx]

Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]

18F20

预层和层[参见14F05, 32C35, 32L10, 54B40, 55N30]

Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]

18F25

代数K-理论与L-理论[参见11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]

Algebraic K-theory and L-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]

18F30

Grothendieck[参见13D15, 16E20, 19Axx]

Grothendieck groups [See also 13D15, 16E20, 19Axx]

18F99

其它

None of the above, but in this section

18Gxx

同调代数[参见13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]

Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]

18G05

射影与内射[参见13C10, 13C11, 16D40, 16D50]

Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]

18G10

预解; 导出函子[参见13D02, 16E05, 18E25]

Resolutions; derived functors [See also 13D02, 16E05, 18E25]

18G15

ExtTor, 推广, Künneth公式[参见55U25]

Ext and Tor, generalizations, Künneth formula [See also 55U25]

18G20

同调维数[参见13D05, 16E10]

Homological dimension [See also 13D05, 16E10]

18G25

相关同调代数, 射影类

Relative homological algebra, projective classes

18G30

单纯集, 单纯对象(在一个范畴中)[参见55U10]

Simplicial sets, simplicial objects (in a category) [See also 55U10]

18G35

链复形[参见18E30, 55U15]

Chain complexes [See also 18E30, 55U15]

18G40

谱序列, 超上同调[参见55Txx]

Spectral sequences, hypercohomology [See also 55Txx]

18G50

Abel同调代数

Nonabelian homological algebra

18G55

同伦代数

Homotopical algebra

18G60

其它()同调理论[参见19D55, 46L80, 58J20, 58J22]

Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]

18G99

其它

None of the above, but in this section

19-XX

K-理论[参见16E20, 18F25]

K-theory [See also 16E20, 18F25]

19-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

19-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

19-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

19-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

19-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

19-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

19Axx

Grothendieck群和K0[参见13D15, 18F30]

Grothendieck groups and K0 [See also 13D15, 18F30]

19A13

射影模的稳定性[参见13C10]

Stability for projective modules [See also 13C10]

19A15

有效生成

Efficient generation

19A22

Frobenius归纳法, Burnside环与表示环

Frobenius induction, Burnside and representation rings

19A31

群环和整环的K0

K0 of group rings and orders

19A49

其它环的K0

K0 of other rings

19A99

其它

None of the above, but in this section

19Bxx

Whitehead群和K1

Whitehead groups and K1

19B10

稳定区域条件

Stable range conditions

19B14

线性群的稳定性

Stability for linear groups

19B28

群环和整环的K1[参见57Q10]

K1 of group rings and orders [See also 57Q10]

19B37

同余子群问题[参见20H05]

Congruence subgroup problems [See also 20H05]

19B99

其它

None of the above, but in this section

19Cxx

Steinberg群和K2

Steinberg groups and K2

19C09

中心扩张与Schur乘子

Central extensions and Schur multipliers

19C20

K2的符号, 表达式和稳定性

Symbols, presentations and stability of K2

19C30

K2Brauer

K2 and the Brauer group

19C40

K2的分割

Excision for K2

19C99

其它

None of the above, but in this section

19Dxx

高等代数K-理论

Higher algebraic K-theory

19D06

Q-构造和附加构造

Q- and plus-constructions

19D10

空间的代数K-理论

Algebraic K-theory of spaces

19D23

对称单项范畴[参见18D10]

Symmetric monoidal categories [See also 18D10]

19D25

Karoubi-Villamayor-Gersten K-理论

Karoubi-Villamayor-Gersten K-theory

19D35

K-理论, NK与幂零

Negative K-theory, NK and Nil

19D45

高等符号, Milnor K-理论

Higher symbols, Milnor K-theory

19D50

环的高等K-理论的计算[参见13D15, 16E20]

Computations of higher K-theory of rings [See also 13D15, 16E20]

19D55

K-理论与同调; 循环同调与上同调[参见18G60]

K-theory and homology; cyclic homology and cohomology [See also 18G60]

19D99

其它

None of the above, but in this section

19Exx

几何中的K-理论

K-theory in geometry

19E08

概型的K-理论[参见14C35]

K-theory of schemes [See also 14C35]

19E15

代数闭链和主上同调[参见14C25, 14C35]

Algebraic cycles and motivic cohomology [See also 14C25, 14C35]

19E20

与上同调理论的关系[参见14Fxx]

Relations with cohomology theories [See also 14Fxx]

19E99

其它

None of the above, but in this section

19Fxx

数论中的K-理论[参见11R70, 11S70]

K-theory in number theory [See also 11R70, 11S70]

19F05

一般类域理论[参见11G45]

Generalized class field theory [See also 11G45]

19F15

符号与算术[参见11R37]

Symbols and arithmetic [See also 11R37]

19F27

Étale上同调, 高等调节器, ζ函数和L-函数[参见11G40, 11R42, 11S40, 14F20, 14G10]

Étale cohomology, higher regulators, zeta and L-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]

19F99

其它

None of the above, but in this section

19Gxx

型的K-理论[参见11Exx]

K-theory of forms [See also 11Exx]

19G05

二次模的稳定性

Stability for quadratic modules

19G12

环的Witt[参见11E81]

Witt groups of rings [See also 11E81]

19G24

群环的L-理论[参见11E81]

L-theory of group rings [See also 11E81]

19G38

Hermite K-理论, 与环的K-理论的关系

Hermitian K-theory, relations with K-theory of rings

19G99

其它

None of the above, but in this section

19Jxx

来自拓扑的障碍

Obstructions from topology

19J05

K0中的有限性和其它障碍

Finiteness and other obstructions in K0

19J10

Whitehead(和有关的)

Whitehead (and related) torsion

19J25

换球术障碍[参见57R67]

Surgery obstructions [See also 57R67]

19J35

群作用的障碍

Obstructions to group actions

19J99

其它

None of the above, but in this section

19Kxx

K-理论与算子代数[主要见46L80, 46M20]

K-theory and operator algebras [See mainly 46L80, and also 46M20]

19K14

作为有序群的K0,

K0 as an ordered group, traces

19K33

EXTK-同调[参见55N22]

EXT and K-homology [See also 55N22]

19K35

Kasparov(KK-理论)[参见58J22]

Kasparov theory (KK-theory) [See also 58J22]

19K56

指标理论[参见58J20, 58J22]

Index theory [See also 58J20, 58J22]

19K99

其它

None of the above, but in this section

19Lxx

拓扑K-理论[参见55N15, 55R50, 55S25]

Topological K-theory [See also 55N15, 55R50, 55S25]

19L10

Riemann-Roch定理, Chern特征标

Riemann-Roch theorems, Chern characters

19L20

J-同态, Adams运算[参见55Q50]

J-homomorphism, Adams operations [See also 55Q50]

19L41

连通K-理论, 配边[参见55N22]

Connective K-theory, cobordism [See also 55N22]

19L47

等变K-理论[参见55N91, 55P91, 55Q91, 55R91, 55S91]

Equivariant K-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]

19L50

K-理论;微分K-理论

Twisted K-theory; differential K-theory

19L64

计算, 几何应用

Computations, geometric applications

19L99

其它

None of the above, but in this section

19Mxx

K-理论的各种应用

Miscellaneous applications of K-theory

19M05

K-理论的各种应用

Miscellaneous applications of K-theory

19M99

其它

None of the above, but in this section

20-XX

群论及其推广

Group theory and generalizations

20-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

20-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

20-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

20-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

20-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

20-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

20Axx

基础

Foundations

20A05

公理系统与基本性质

Axiomatics and elementary properties

20A10

元数学的考虑(字问题, 20F10)

Metamathematical considerations (For word problems, see 20F10)

20A15

逻辑在群论中的应用

Applications of logic to group theory

20A99

其它

None of the above, but in this section

20Bxx

置换群

Permutation groups

20B05

有限群的一般理论

General theory for finite groups

20B07

无限群的一般理论

General theory for infinite groups

20B10

特征定理

Characterization theorems

20B15

本原群

Primitive groups

20B20

多重可迁有限群

Multiply transitive finite groups

20B22

多重可迁无限群

Multiply transitive infinite groups

20B25

代数, 几何或组合结构的有限自同构群[参见05Bxx, 12F10, 20G40, 20H30, 51-XX]

Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]

20B27

无限自同构群[参见12F10]

Infinite automorphism groups [See also 12F10]

20B30

对称群

Symmetric groups

20B35

对称群的子群

Subgroups of symmetric groups

20B40

计算方法

Computational methods

20B99

其它

None of the above, but in this section

20Cxx

群表示理论[参见19A22(表示环和Burnside)]

Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]

20C05

有限群的群环及其模[参见16S34]

Group rings of finite groups and their modules [See also 16S34]

20C07

无限群的群环及其模[参见16S34]

Group rings of infinite groups and their modules [See also 16S34]

20C08

Hecke代数及其表示

Hecke algebras and their representations

20C10

有限群的整数表示

Integral representations of finite groups

20C11

有限群的p-进表示

p-adic representations of finite groups

20C12

无限群的整数表示

Integral representations of infinite groups

20C15

一般表示与特征标

Ordinary representations and characters

20C20

模表示与特征标

Modular representations and characters

20C25

射影表示与乘子

Projective representations and multipliers

20C30

有限对称群的表示

Representations of finite symmetric groups

20C32

无限对称群的表示

Representations of infinite symmetric groups

20C33

有限Lie型群的表示

Representations of finite groups of Lie type

20C34

散在群的表示

Representations of sporadic groups

20C35

群表示理论在物理中的应用

Applications of group representations to physics

20C40

计算方法

Computational methods

20C99

其它

None of the above, but in this section

20Dxx

抽象有限群

Abstract finite groups

20D05

有限单群及其分类

Finite simple groups and their classification

20D06

单群: 交错群和Lie型群[参见20Gxx]

Simple groups: alternating groups and groups of Lie type [See also 20Gxx]

20D08

单群: 分散群(零星群)

Simple groups: sporadic groups

20D10

可解群, 形成理论, Schunck, Fitting, π-长度, [参见20F17]

Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks [See also 20F17]

20D15

幂零群, p-

Nilpotent groups, p-groups

20D20

Sylow, Sylow性质, π, π结构

Sylow subgroups, Sylow properties, π-groups, π-structure

20D25

特殊子群(FrattiniFitting)

Special subgroups (Frattini, Fitting, etc.)

20D30

子群的列和格

Series and lattices of subgroups

20D35

次正规子群

Subnormal subgroups

20D40

子群的积

Products of subgroups

20D45

自同构

Automorphisms

20D60

算术与组合问题

Arithmetic and combinatorial problems

20D99

其它

None of the above, but in this section

20Exx

无限群或有限群的结构与分类

Structure and classification of infinite or finite groups

20E05

自由非Abel

Free nonabelian groups

20E06

自由积, 有融合的自由积, Higman-Neumann-Neumann扩张及其推广

Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations

20E07

子群定理; 子群增长性

Subgroup theorems; subgroup growth

20E08

作用于树上的群[参见20F65]

Groups acting on trees [See also 20F65]

20E10

群的拟簇和簇

Quasivarieties and varieties of groups

20E15

子群的链与格, 次正规子群[参见20F22]

Chains and lattices of subgroups, subnormal subgroups [See also 20F22]

20E18

极限, 投射有限群

Limits, profinite groups

20E22

扩张, 环积与其它合成[参见20J05]

Extensions, wreath products, and other compositions [See also 20J05]

20E25

局部性质

Local properties

20E26

剩余性质及其推广; 剩余有限群

Residual properties and generalizations; residually finite groups

20E28

极大子群

Maximal subgroups

20E32

单群[参见20D05]

Simple groups [See also 20D05]

20E34

一般结构定理

General structure theorems

20E36

无限群的自同构(有限群的自同构, 20D45)

Automorphisms of infinite groups (For automorphisms of finite groups, see 20D45)

20E42

BN对的群; 造型[参见51E24]

Groups with a BN-pair; buildings [See also 51E24]

20E45

共轭类

Conjugacy classes

20E99

其它

None of the above, but in this section

20Fxx

无限或有限群的特殊方面

Special aspects of infinite or finite groups

20F05

生成元, 关系和预命题

Generators, relations, and presentations

20F06

消去理论; van Kampen图表的应用[参见57M05]

Cancellation theory; application of van Kampen diagrams [See also 57M05]

20F10

字问题, 其它判定问题, 与逻辑和自动机的关系[参见03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]

Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]

20F11

有限Morley秩的群[参见03C45, 03C60]

Groups of finite Morley rank [See also 03C45, 03C60]

20F12

换位子演算

Commutator calculus

20F14

导出列, 中心列及其推广

Derived series, central series, and generalizations

20F16

可解群, 超可解群[参见20D10]

Solvable groups, supersolvable groups [See also 20D10]

20F17

群的形成, Fitting[参见20D10]

Formations of groups, Fitting classes [See also 20D10]

20F18

幂零群[参见20D15]

Nilpotent groups [See also 20D15]

20F19

可解群与幂零群的推广

Generalizations of solvable and nilpotent groups

20F22

用子群链定义的其它群类

Other classes of groups defined by subgroup chains

20F24

FC-群及其推广

FC-groups and their generalizations

20F28

群的自同构群[参见20E36]

Automorphism groups of groups [See also 20E36]

20F29

作为代数系统自同构群的群表示

Representations of groups as automorphism groups of algebraic systems

20F34

基本群及其自同构[参见57M05, 57Sxx]

Fundamental groups and their automorphisms [See also 57M05, 57Sxx]

20F36

辫群; Artin

Braid groups; Artin groups

20F38

与拓扑或分析有关的其它群

Other groups related to topology or analysis

20F40

结合Lie结构

Associated Lie structures

20F45

Engel条件

Engel conditions

20F50

周期群; 局部有限群

Periodic groups; locally finite groups

20F55

反射群和Coxeter[参见22E40, 51F15]

Reflection and Coxeter groups [See also 22E40, 51F15]

20F60

有序群[主要见06F15]

Ordered groups [See mainly 06F15]

20F65

几何群论[参见05C25, 20E08, 57Mxx]

Geometric group theory [See also 05C25, 20E08, 57Mxx]

20F67

双曲群和非正曲线群

Hyperbolic groups and nonpositively curved groups

20F69

群的渐近性质

Asymptotic properties of groups

20F70

群上的代数几何; 群上方程

Algebraic geometry over groups; equations over groups

20F99

其它

None of the above, but in this section

20Gxx

线性代数群及相关课题(算术理论, 11E57, 11H56; 几何理论, 14Lxx, 22Exx; 表示论中的其它方法, 15A30, 22E45, 22E46, 22E47, 22E50, 22E55)

Linear algebraic groups and related topics (For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55)

20G05

表示理论

Representation theory

20G07

结构理论

Structure theory

20G10

上同调论

Cohomology theory

20G15

任意域上的线性代数群

Linear algebraic groups over arbitrary fields

20G20

实数, 复数和四元数体上的线性代数群

Linear algebraic groups over the reals, the complexes, the quaternions

20G25

局部域上的线性代数群及其整群

Linear algebraic groups over local fields and their integers

20G30

整体域上的线性代数群及其整群

Linear algebraic groups over global fields and their integers

20G35

赋值向量环和其它环及概型上的线性代数群

Linear algebraic groups over adèles and other rings and schemes

20G40

有限域上的线性代数群

Linear algebraic groups over finite fields

20G41

例外群

Exceptional groups

20G42

量子群(量子函数代数)及其表示[参见16T20, 17B37, 81R50]

Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]

20G43

Schurq-Schur代数

Schur and q-Schur algebras

20G44

Kac-Moody

Kac-Moody groups

20G45

物理上的应用

Applications to physics

20G99

其它

None of the above, but in this section

20Hxx

其它矩阵群[参见15A30]

Other groups of matrices [See also 15A30]

20H05

么模群, 同余子群[参见11F06, 19B37, 22E40, 51F20]

Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]

20H10

Fuchs群及其推广[参见11F06, 22E40, 30F35, 32Nxx]

Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

20H15

其它几何群, 包括结晶体群[参见51-XX, 特别是51F1582D25]

Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]

20H20

域上的其它矩阵群

Other matrix groups over fields

20H25

环上的其它矩阵群

Other matrix groups over rings

20H30

有限域上的其它矩阵群

Other matrix groups over finite fields

20H99

其它

None of the above, but in this section

20Jxx

与同调代数和范畴论的联系

Connections with homological algebra and cate­gory theory

20J05

群论中的同调方法

Homological methods in group theory

20J06

群的上同调

Cohomology of groups

20J15

群的范畴

Category of groups

20J99

其它

None of the above, but in this section

20Kxx

Abel

Abelian groups

20K01

有限Abel[和集, 11B1311P70]

Finite abelian groups [For sumsets, see 11B13 and 11P70]

20K10

挠群, 准素群及其广义准素群

Torsion groups, primary groups and generalized primary groups

20K15

无挠群, 有限秩

Torsion-free groups, finite rank

20K20

无挠群, 无限秩

Torsion-free groups, infinite rank

20K21

混合群

Mixed groups

20K25

直和、直积等

Direct sums, direct products, etc.

20K27

子群

Subgroups

20K30

自同构、同态、自同态等

Automorphisms, homomorphisms, endomorphisms, etc.

20K35

扩张

Extensions

20K40

同调方法与范畴方法

Homological and categorical methods

20K45

拓扑方法[参见22A05, 22B05]

Topological methods [See also 22A05, 22B05]

20K99

其它

None of the above, but in this section

20Lxx

广群(比如: 所有态射是同构的小范畴)(具有单个二元运算的集合, 20N02; 拓扑广群, 22A22, 58H05)

Groupoids (i.e. small categories in which all morphisms are isomorphisms) (For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05)

20L05

广群(比如: 所有态射是同构的小范畴)(具有单个二元运算的集合, 20N02; 拓扑广群, 22A22, 58H05)

Groupoids (i.e. small categories in which all morphisms are isomorphisms)(For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05)

20L99

其它

None of the above, but in this section

20Mxx

半群

Semigroups

20M05

自由半群, 生成元和关系, 字问题

Free semigroups, generators and relations, word problems

20M07

半群的簇和伪簇

Varieties and pseudovarieties of semigroups

20M10

一般结构理论

General structure theory

20M11

根理论

Radical theory

20M12

理想理论

Ideal theory

20M13

幺半群的算术理论

Arithmetic theory of monoids

20M14

交换半群

Commutative semigroups

20M15

半群的映射

Mappings of semigroups

20M17

正则半群

Regular semigroups

20M18

逆半群

Inverse semigroups

20M19

纯正半群

Orthodox semigroups

20M20

变换半群等[参见47D03, 47H20, 54H15]

Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]

20M25

半群环, 环的乘法半群[参见16S36, 16Y60]

Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]

20M30

半群的表示; 集上半群的作用

Representation of semigroups; actions of semigroups on sets

20M32

代数幺半群

Algebraic monoids

20M35

自动机理论中的半群、语言学等[参见03D05, 68Q70, 68T50]

Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]

20M50

半群与同调代数和范畴论的联系

Connections of semigroups with homological algebra and category theory

20M99

其它

None of the above, but in this section

20Nxx

群的其它推广

Other generalizations of groups

20N02

具有单个二元运算的集合(广群)

Sets with a single binary operation (groupoids)

20N05

, 拟群[参见05Bxx]

Loops, quasigroups [See also 05Bxx]

20N10

三元系(堆、半堆、广堆等)

Ternary systems (heaps, semiheaps, heapoids, etc.)

20N15

n-元系(n≥3)

n-ary systems (n≥3)

20N20

超群

Hypergroups

20N25

模糊群[参见03E72]

Fuzzy groups [See also 03E72]

20N99

其它

None of the above, but in this section

20Pxx

群论中的概率方法[参见60Bxx]

Probabilistic methods in group theory [See also 60Bxx]

20P05

群论中的概率方法[参见60Bxx]

Probabilistic methods in group theory [See also 60Bxx]

20P99

其它

None of the above, but in this section

22-XX

拓扑群, Lie(变换群, 54H15, 57Sxx, 58-XX; 抽象调和分析, 43-XX)

Topological groups, Lie groups (For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX)

22-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

22-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

22-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

22-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

22-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

22-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

22Axx

拓扑与微分代数系统(拓扑环和域, 12Jxx, 13Jxx, 16W80)

Topological and differentiable algebraic systems (For topological rings and fields, see 12Jxx, 13Jxx, 16W80)

22A05

一般拓扑群的结构

Structure of general topological groups

22A10

一般拓扑群上的分析

Analysis on general topological groups

22A15

拓扑半群的结构

Structure of topological semigroups

22A20

拓扑半群上的分析

Analysis on topological semigroups

22A22

拓扑广群(包括可微广群和Lie广群)[参见58H05]

Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]

22A25

一般拓扑群和拓扑半群的表示

Representations of general topological groups and semigroups

22A26

拓扑半格, 拓扑格和应用[参见06B30, 06B35, 06F30]

Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]

22A30

其它拓扑代数系统及其表示

Other topological algebraic systems and their representations

22A99

其它

None of the above, but in this section

22Bxx

局部紧Abel(LCA)

Locally compact abelian groups (LCA groups)

22B05

LCA群的一般性质和结构

General properties and structure of LCA groups

22B10

LCA群的群代数的结构

Structure of group algebras of LCA groups

22B99

其它

None of the above, but in this section

22Cxx

紧群

Compact groups

22C05

紧群

Compact groups

22C99

其它

None of the above, but in this section

22Dxx

局部紧群及其代数

Locally compact groups and their algebras

22D05

局部紧群的一般性质和结构

General properties and structure of locally compact groups

22D10

局部紧群的酉表示

Unitary representations of locally compact groups

22D12

局部紧群的其它表示

Other representations of locally compact groups

22D15

局部紧群的群代数

Group algebras of locally compact groups

22D20

群代数的表示

Representations of group algebras

22D25

在群表示中的C*-代数和W*-代数[参见46Lxx]

C*-algebras and W*-algebras in relation to group represen­tations [See also 46Lxx]

22D30

诱导表示

Induced representations

22D35

对偶定理

Duality theorems

22D40

群上的遍历理论[参见28Dxx]

Ergodic theory on groups [See also 28Dxx]

22D45

局部紧群的自同构群

Automorphism groups of locally compact groups

22D99

其它

None of the above, but in this section

22Exx

Lie(Lie群和齐性空间的拓扑, 57Sxx, 57Txx; 分析方面, 43A80, 43A85, 43A90)

Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90)

22E05

局部Lie[参见34-XX, 35-XX, 58H05]

Local Lie groups [See also 34-XX, 35-XX, 58H05]

22E10

Lie群的一般性质和结构[参见32M05]

General properties and structure of complex Lie groups [See also 32M05]

22E15

Lie群的一般性质和结构

General properties and structure of real Lie groups

22E20

其它Lie群的一般性质和结构

General properties and structure of other Lie groups

22E25

幂零Lie群与可解Lie

Nilpotent and solvable Lie groups

22E27

幂零Lie群与可解Lie群的表示(特殊轨道积分、非I型表示等)

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)

22E30

Lie群与复Lie群上的分析[参见33C80, 43-XX]

Analysis on real and complex Lie groups [See also 33C80, 43-XX]

22E35

p-Lie群上的分析

Analysis on p-adic Lie groups

22E40

Lie群的离散子群[参见20Hxx, 32Nxx]

Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

22E41

连续上同调[参见57R32, 57Txx, 58H10]

Continuous cohomology [See also 57R32, 57Txx, 58H10]

22E43

Lorentz群的结构与表示

Structure and representation of the Lorentz group

22E45

实域上Lie群与线性代数群的表示:解析方法[纯代数理论, 20G05]

Representations of Lie and linear algebraic groups over real fields: analytic methods (For the purely algebraic theory, see 20G05)

22E46

半单Lie群及其表示

Semisimple Lie groups and their representations

22E47

Lie群和实代数群的表示: 代数方法(Verma模等)[参见17B10]

Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]

22E50

局部域上Lie群和线性代数群的表示[参见20G05]

Representations of Lie and linear algebraic groups over local fields [See also 20G05]

22E55

整体域和赋值向量环上的Lie群和线性代数群的表示[参见20G05]

Representations of Lie and linear algebraic groups over global fields and adèle rings [See also 20G05]

22E57

几何Langlands程序:表示理论方面[参见14D24]

Geometric Langlands program: representation theoretic aspects [See also 14D24]

22E60

Lie群的Lie代数(Lie代数的代数理论, 17Bxx)

Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)

22E65

无限维Lie群及其Lie代数; 一般性质[参见17B65, 58B25, 58H05]

Infinite-dimensional Lie groups and their Lie algebras; general properties [See also 17B65, 58B25, 58H05]

22E66

无限维Lie群的分析和表示

Analysis on and representations of infinite-dimensional Lie groups

22E67

圈群及有关构造, 群论处理[参见58D05]

Loop groups and related constructions, group-theoretic treatment [See also 58D05]

22E70

Lie群在物理上的应用; 显式表示[参见81R05, 81R10]

Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]

22E99

其它

None of the above, but in this section

22Fxx

非紧变换群

Noncompact transformation groups

22F05

群和伪群作用的一般理论(具有作用空间的拓扑性质, 57S20)

General theory of group and pseudogroup actions (For topological properties of spaces with an action, see 57S20)

22F10

可测群作用[参见22D40, 28Dxx, 37Axx]

Measurable group actions [See also 22D40, 28Dxx, 37Axx]

22F30

齐性空间(一般作用在流形或保几何结构, 57M60, 57Sxx; Lie群的离散子群, 特别见22E40)

Homogeneous spaces (For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40)

22F50

作为其它结构自同构的群

Groups as automorphisms of other structures

22F99

其它

None of the above, but in this section

26-XX

实函数[参见54C30]

Real functions [See also 54C30]

26-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

26-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

26-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

26-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

26-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

26-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

26Axx

一元函数

Functions of one variable

26A03

基础: 极限及其推广, 初等线拓扑

Foundations: limits and generalizations, elementary topology of the line

26A06

一元微积分

One-variable calculus

26A09

初等函数

Elementary functions

26A12

函数增长率, 无穷阶, 慢变函数[参见26A48]

Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]

26A15

连续性及有关问题(连续性模、半连续性模、间断模等)(Fourier系数确定的性质, 42A16; 由逼近性确定的性质, 41A25, 41A27)

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) (For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27)

26A16

Lipschitz(Hölder)

Lipschitz (Hölder) classes

26A18

迭代[参见37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]

Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]

26A21

实函数分类; 集合与函数的Baire分类[参见03E15, 28A05, 54C50]

Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50]

26A24

微分法(一元函数): 一般理论, 广义导数, 中值定理[参见28A15]

Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]

26A27

不可微性(不可微函数, 不可微点), 不连续导数

Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives

26A30

奇异函数, Cantor函数, 具有其它特殊性质的函数

Singular functions, Cantor functions, functions with other special properties

26A33

分数次导数和分数次积分

Fractional derivatives and integrals

26A36

反微分法

Antidifferentiation

26A39

Denjoy积分和Perron积分, 其它特殊积分

Denjoy and Perron integrals, other special integrals

26A42

Riemann, StieltjesLebesgue型积分[参见28-XX]

Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]

26A45

有界变差函数, 推广

Functions of bounded variation, generalizations

26A46

绝对连续函数

Absolutely continuous functions

26A48

单调函数, 推广

Monotonic functions, generalizations

26A51

凸性, 推广

Convexity, generalizations

26A99

其它

None of the above, but in this section

26Bxx

多元函数

Functions of several variables

26B05

连续性和微分法问题

Continuity and differentiation questions

26B10

隐函数定理, Jacobi行列式, 多元变换

Implicit function theorems, Jacobians, transformations with several variables

26B12

向量函数的微积分

Calculus of vector functions

26B15

积分法: 长度, 面积, 体积[参见28A75, 51M25]

Integration: length, area, volume [See also 28A75, 51M25]

26B20

积分公式(StokesGaussGreen)

Integral formulas (Stokes, Gauss, Green, etc.)

26B25

凸性, 推广

Convexity, generalizations

26B30

绝对连续函数, 有界变差函数

Absolutely continuous functions, functions of bounded variation

26B35

多元函数的特性、Hölder条件等

Special properties of functions of several variables, Hölder conditions, etc.

26B40

函数的表示和叠加

Representation and superposition of functions

26B99

其它

None of the above, but in this section

26Cxx

多项式, 有理函数

Polynomials, rational functions

26C05

多项式: 解析性质等[参见12Dxx, 12Exx]

Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]

26C10

多项式: 零点位置[参见12D10, 30C15, 65H05]

Polynomials: location of zeros [See also 12D10, 30C15, 65H05]

26C15

有理函数[参见14Pxx]

Rational functions [See also 14Pxx]

26C99

其它

None of the above, but in this section

26Dxx

不等式(极大函数不等式, 42B25; 泛函不等式, 39B72; 概率不等式, 60E15)

Inequalities (For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for proba­bilistic inequalities, see 60E15)

26D05

三角函数与多项式不等式

Inequalities for trigonometric functions and polynomials

26D07

涉及其它类型函数的不等式

Inequalities involving other types of functions

26D10

涉及求导、微分和积分算子的不等式

Inequalities involving derivatives and differential and integral operators

26D15

和、级数和积分不等式

Inequalities for sums, series and integrals

26D20

其它解析不等式

Other analytical inequalities

26D99

其它

None of the above, but in this section

26Exx

杂题[参见58Cxx]

Miscellaneous topics [See also 58Cxx]

26E05

实解析函数[参见32B05, 32C05]

Real-analytic functions [See also 32B05, 32C05]

26E10

C-函数, 拟解析函数[参见58C25]

C-functions, quasi-analytic functions [See also 58C25]

26E15

无限维空间中函数的微积分[参见46G05, 58Cxx]

Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]

26E20

在无限维空间中取值的函数的微积分[参见46E40, 46G10, 58Cxx]

Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]

26E25

集值函数[参见28B20, 54C60](非光滑分析, 49J52, 58Cxx, 90Cxx)

Set-valued functions [See also 28B20, 54C60] (For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx)

26E30

Archimedes分析[参见12J25]

Non-Archimedean analysis [See also 12J25]

26E35

非标准分析[参见03H05, 28E05, 54J05]

Nonstandard analysis [See also 03H05, 28E05, 54J05]

26E40

构造性实分析[参见03F60]

Constructive real analysis [See also 03F60]

26E50

模糊实分析[参见03E72, 28E10]

Fuzzy real analysis [See also 03E72, 28E10]

26E60

平均[参见47A64]

Means [See also 47A64]

26E70

时间尺度或测度链上的实分析 (时间尺度或测度链上的动力学方程, 34N05)

Real analysis on time scales or measure chains (For dynamic equations on time scales or measure chains see 34N05)

26E99

其它

None of the above, but in this section

28-XX

测度与积分(流形上的分析, 58-XX)

Measure and integration (For analysis on manifolds, see 58-XX)

28-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

28-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

28-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

28-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

28-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

28-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

28Axx

经典测度论

Classical measure theory

28A05

集合类(Borel域、σ-环等), 可测集, Suslin, 解析集[参见03E15, 26A21, 54H05]

Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

28A10

实值或复值集合函数

Real- or complex-valued set functions

28A12

容度, 测度, 外测度, 容量

Contents, measures, outer measures, capacities

28A15

抽象微分理论, 集合函数的微分法[参见26A24]

Abstract differentiation theory, differentiation of set functions [See also 26A24]

28A20

可测函数与不可测函数, 可测函数序列, 收敛方式

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

28A25

关于测度及其它集合函数的积分法

Integration with respect to measures and other set functions

28A33

测度空间, 测度的收敛性[参见46E27, 60Bxx]

Spaces of measures, convergence of measures [See also 46E27, 60Bxx]

28A35

积空间中的测度与积分

Measures and integrals in product spaces

28A50

测度的积分法与测度的蜕变

Integration and disintegration of measures

28A51

提升理论[参见46G15]

Lifting theory [See also 46G15]

28A60

Boole环上的测度, 测度代数[参见54H10]

Measures on Boolean rings, measure algebras [See also 54H10]

28A75

长度, 面积, 体积, 其它几何测度论[参见26B15, 49Q15]

Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

28A78

Hausdorff测度和填装测度

Hausdorff and packing measures

28A80

分形[参见37Fxx]

Fractals [See also 37Fxx]

28A99

其它

None of the above, but in this section

28Bxx

抽象空间中取值的集函数、测度与积分

Set functions, measures and integrals with values in abstract spaces

28B05

向量值集函数、测度与积分[参见46G10]

Vector-valued set functions, measures and integrals [See also 46G10]

28B10

群或半群值集函数、测度与积分

Group- or semigroup-valued set functions, measures and integrals

28B15

在有序空间中取值的集函数、测度与积分

Set functions, measures and integrals with values in ordered spaces

28B20

集值集函数与测度; 集值函数的积分法; 可测选择[参见26E25, 54C60, 54C65, 91B14]

Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14]

28B99

其它

None of the above, but in this section

28Cxx

附加结构空间上的集函数与测度[参见46G12, 58C35, 58D20]

Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]

28C05

借助线性泛函的积分理论(Radon测度、Daniell积分等), 表示集函数与测度

Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures

28C10

拓扑群或半群上的集函数与测度, Haar测度, 不变测度[参见22Axx, 43A05]

Set functions and measures on topological groups or semigroup, Haar measures, invariant measures [See also 22Axx, 43A05]

28C15

拓扑空间上的集函数与测度(测度的正则性等)

Set functions and measures on topological spaces (regularity of measures, etc.)

28C20

无限维空间中的集函数, 测度与积分(Wiener测度、Gauss测度等)[参见46G12, 58C35, 58D20, 60B11]

Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]

28C99

其它

None of the above, but in this section

28Dxx

测度论的遍历理论[参见11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]

Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]

28D05

保测度变换

Measure-preserving transformations

28D10

保测度变换的单参数连续族

One-parameter continuous families of measure-preserving transformations

28D15

一般保测度变换群

General groups of measure-preserving transformations

28D20

熵和其它不变量

Entropy and other invariants

28D99

其它

None of the above, but in this section

28Exx

测度论中的杂题

Miscellaneous topics in measure theory

28E05

非标准测度论[参见03H05, 26E35]

Nonstandard measure theory [See also 03H05, 26E35]

28E10

模糊测度论[参见03E72, 26E50, 94D05]

Fuzzy measure theory [See also 03E72, 26E50, 94D05]

28E15

与逻辑及集合论的其它联系

Other connections with logic and set theory

28E99

其它

None of the above, but in this section

30-XX

单复变量函数(流形上的分析, 58-XX)

Functions of a complex variable (For analysis on manifolds, see 58-XX)

30-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, biblio­graphies, etc.)

30-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

30-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

30-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

30-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

30-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

30Axx

一般性质

General properties

30A05

复函数的单演性质(包括多因子单演函数和网状单演函数)

Monogenic properties of complex functions (including polygenic and areolar monogenic functions)

30A10

复域中的不等式

Inequalities in the complex domain

30A99

其它

None of the above, but in this section

30Bxx

级数展开

Series expansions

30B10

幂级数(包括缺项级数)

Power series (including lacunary series)

30B20

随机幂级数

Random power series

30B30

幂级数的边界特性, 超收敛性

Boundary behavior of power series, over-convergence

30B40

解析延拓

Analytic continuation

30B50

Dirichlet级数与其它级数展开, 指数级数[参见11M41, 42-XX]

Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]

30B60

完备性问题, 函数系统的闭包

Completeness problems, closure of a system of functions

30B70

连分式[参见11A55, 40A15]

Continued fractions [See also 11A55, 40A15]

30B99

其它

None of the above, but in this section

30Cxx

几何函数论

Geometric function theory

30C10

多项式

Polynomials

30C15

多项式、有理函数及其它解析函数的零点(例如: 具有有界Dirichlet积分的函数的零点)(代数理论, 12D10; 实方法, 26C10)

Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) (For algebraic theory, see 12D10; for real methods, see 26C10)

30C20

特殊域的共形映射

Conformal mappings of special domains

30C25

共形映射理论中的覆盖定理

Covering theorems in conformal mapping theory

30C30

共形映射理论中的数值方法[参见65E05]

Numerical methods in conformal mapping theory [See also 65E05]

30C35

共形映射的一般理论

General theory of conformal mappings

30C40

核函数及其应用

Kernel functions and applications

30C45

特殊单叶和多叶函数类(星形的、凸的、有界旋度等)

Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

30C50

单叶和多叶函数的系数问题

Coefficient problems for univalent and multivalent functions

30C55

单叶和多叶函数的一般理论

General theory of univalent and multivalent functions

30C62

平面中的拟共形映射

Quasiconformal mappings in the plane

30C65

Rn中的拟共形映射, 其它推广

Quasiconformal mappings in Rn, other generalizations

30C70

共形和拟共形映射的极值问题, 变分法

Extremal problems for conformal and quasiconformal mappings, variational methods

30C75

共形和拟共形映射的极值问题, 其它方法

Extremal problems for conformal and quasiconformal mappings, other methods

30C80

极大值原理; Schwarz引理, Lindelöf原理, 模拟和推广; 从属运算

Maximum principle; Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination

30C85

复平面中的容量与调和测度[参见31A15]

Capacity and harmonic measure in the complex plane [See also 31A15]

30C99

其它

None of the above, but in this section

30Dxx

整函数与亚纯函数, 及相关论题

Entire and meromorphic functions, and related topics

30D05

复域中的泛函方程, 解析函数的迭代与合成[参见34Mxx, 37Fxx, 39-XX]

Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]

30D10

整函数的级数与积分表示

Representations of entire functions by series and integrals

30D15

特殊整函数类及其增长估计

Special classes of entire functions and growth estimates

30D20

整函数, 一般理论

Entire functions, general theory

30D30

亚纯函数, 一般理论

Meromorphic functions, general theory

30D35

值分布, Nevanlinna理论

Distribution of values, Nevanlinna theory

30D40

聚类集合, 素端, 边界特性

Cluster sets, prime ends, boundary behavior

30D45

Bloch函数, 正规函数, 正规族

Bloch functions, normal functions, normal families

30D60

拟解析函数与其它函数类

Quasi-analytic and other classes of functions

30D99

其它

None of the above, but in this section

30Exx

复域中分析的杂题

Miscellaneous topics of analysis in the complex domain

30E05

矩问题, 插值问题

Moment problems, interpolation problems

30E10

复域中的逼近

Approximation in the complex domain

30E15

复域中的渐近表示

Asymptotic representations in the complex domain

30E20

积分法, Cauchy型积分, 解析函数的积分表示[参见45Exx]

Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]

30E25

边值问题[参见45Exx]

Boundary value problems [See also 45Exx]

30E99

其它

None of the above, but in this section

30Fxx

Riemann曲面

Riemann surfaces

30F10

Riemann曲面和单值化[参见14H15, 32G15]

Compact Riemann surfaces and uniformization [See also 14H15, 32G15]

30F15

Riemann曲面上的调和函数

Harmonic functions on Riemann surfaces

30F20

Riemann曲面上的分类理论

Classification theory of Riemann surfaces

30F25

理想边界理论

Ideal boundary theory

30F30

Riemann曲面上的微分

Differentials on Riemann surfaces

30F35

Fuchs群和自守函数[参见11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]

Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]

30F40

Klein[参见20H10]

Kleinian groups [See also 20H10]

30F45

共形度量(双曲的, Poncairé, 距离函数)

Conformal metrics (hyperbolic, Poincaré, distance functions)

30F50

Klein曲面

Klein surfaces

30F60

Teichmüller理论[参见32G15]

Teichmüller theory [See also 32G15]

30F99

其它

None of the above, but in this section

30Gxx

广义函数论

Generalized function theory

30G06

Archimedes函数论[参见12J25]; 非标准函数论[参见03H05]

Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]

30G12

细全纯函数与拓扑函数论

Finely holomorphic functions and topological function theory

30G20

BersVekua型推广(伪解析的、p-解析的等)

Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)

30G25

离散解析函数

Discrete analytic functions

30G30

解析函数的其它推广(包括抽象值函数)

Other generalizations of analytic functions (including abstract-valued functions)

30G35

超复变量函数与广义变量函数

Functions of hypercomplex variables and generalized variables

30G99

其它

None of the above, but in this section

30Hxx

解析函数的空间和代数

Spaces and algebras of analytic functions

30H05

有界解析函数

Bounded analytic functions

30H10

Hardy空间

Hardy spaces

30H15

Nevanlinna类和 Smirnov

Nevanlinna class and Smirnov class

30H20

Bergman空间, Fock空间

Bergman spaces, Fock spaces

30H25

Besov空间和Qp-空间

Besov spaces and Qp-spaces

30H30

Bloch空间

Bloch spaces

30H35

BMO-空间

BMO-spaces

30H50

解析函数的代数

Algebras of analytic functions

30H80

Corona理论

Corona theorems

30H99

其它

None of the above, but in this section

30Jxx

圆盘上的函数论

Function theory on the disc

30J05

内函数

Inner functions

30J10

Blaschke

Blaschke products

30J15

奇异内函数

Singular inner functions

30J99

其它

None of the above, but in this section

30Kxx

通用全纯函数

Universal holomorphic functions

30K05

通用Taylor级数

Universal Taylor series

30K10

通用Dirichlet级数

Universal Dirichlet series

30K15

有界通用函数

Bounded universal functions

30K20

复合通用性

Compositional universality

30K99

其它

None of the above, but in this section

30Lxx

度量空间上的分析

Analysis on metric spaces

30L05

度量空间的几何嵌入

Geometric embeddings of metric spaces

30L10

度量空间的拟共形映射

Quasiconformal mappings in metric spaces

30L99

其它

None of the above, but in this section

31-XX

位势论(概率位势论, 60J45)

Potential theory (For probabilistic potential theory, see 60J45)

31-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

31-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

31-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

31-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

31-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

31-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

31Axx

二维理论

Two-dimensional theory

31A05

调和、次调和、上调和函数

Harmonic, subharmonic, superharmonic functions

31A10

积分表示, 积分算子, 积分方程法

Integral representations, integral operators, integral equations methods

31A15

位势和容量, 调和测度, 极值长度[参见30C85]

Potentials and capacity, harmonic measure, extremal length [See also 30C85]

31A20

边界性态(Fatou型定理等)

Boundary behavior (theorems of Fatou type, etc.)

31A25

边值问题和逆问题

Boundary value and inverse problems

31A30

双调和、多调和函数与方程, Poisson方程

Biharmonic, polyharmonic functions and equations, Poisson’s equation

31A35

与微分方程的联系

Connections with differential equations

31A99

其它

None of the above, but in this section

31Bxx

高维理论

Higher-dimensional theory

31B05

调和、次调和、上调和函数

Harmonic, subharmonic, superharmonic functions

31B10

积分表示, 积分算子, 积分方程法

Integral representations, integral operators, integral equations methods

31B15

位势和容量, 极值长度

Potentials and capacities, extremal length

31B20

边值问题和逆问题

Boundary value and inverse problems

31B25

边界性态

Boundary behavior

31B30

双调和、多调和方程与函数

Biharmonic and polyharmonic equations and functions

31B35

与微分方程的联系

Connections with differential equations

31B99

其它

None of the above, but in this section

31Cxx

其它推广

Other generalizations

31C05

调和、次调和、上调和函数

Harmonic, subharmonic, superharmonic functions

31C10

多重调和与多重次调和函数[参见32U05]

Pluriharmonic and plurisubharmonic functions [See also 32U05]

31C12

Riemann流形上位势论[参见53C20; Hodge理论, 58A14]

Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]

31C15

位势和容量

Potentials and capacities

31C20

离散位势论和数值方法

Discrete potential theory and numerical methods

31C25

Dirichlet空间

Dirichlet spaces

31C35

Martin边界理论[参见60J50]

Martin boundary theory [See also 60J50]

31C40

细位势论

Fine potential theory

31C45

其它推广(非线性位势论等)

Other generalizations (nonlinear potential theory, etc.)

31C99

其它

None of the above, but in this section

31Dxx

公理位势论

Axiomatic potential theory

31D05

公理位势论

Axiomatic potential theory

31D99

其它

None of the above, but in this section

31Exx

度量空间的位势论

Potential theory on metric spaces

31E05

度量空间的位势论

Potential theory on metric spaces

31E99

其它

None of the above, but in this section

32-XX

多复变量与解析空间(无限维正则, 46G20, 58B12)

Several complex variables and analytic spaces (For infinite-dimensional holomorphy, see 46G20, 58B12)

32-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

32-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

32-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

32-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

32-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

32-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

32Axx

多复变量全纯函数

Holomorphic functions of several complex variables

32A05

幂级数, 函数级数

Power series, series of functions

32A07

特殊域(Reinhardt, Hartogs, , )

Special domains (Reinhardt, Hartogs, circular, tube)

32A10

全纯函数

Holomorphic functions

32A12

多值函数

Multifunctions

32A15

整函数

Entire functions

32A17

特殊函数族

Special families of functions

32A18

Bloch函数, 正规函数

Bloch functions, normal functions

32A19

函数的正规族, 映射

Normal families of functions, mappings

32A20

亚纯函数

Meromorphic functions

32A22

Nevanlinna理论(局部的); 增长估计; 其它不等式(几何理论, 32H25, 32H30)

Nevanlinna theory (local); growth estimates; other inequalities (For geometric theory, see 32H25, 32H30)

32A25

积分表示; 标准核(SzegöBergman)

Integral representations; canonical kernels (Szegö, Bergman, etc.)

32A26

积分表示, 构造核(例如: Cauchy, Fantappiè型核)

Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)

32A27

剩余的局部理论[参见32C30]

Local theory of residues [See also 32C30]

32A30

单复变量函数理论的其它推广(还必须在30-XX中至少指定一个分类号)(多超复变量函数, 30G35)

Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) (For functions of several hypercomplex variables, see 30G35)

32A35

Hp空间, Nevanlinna空间[参见32M15, 42B30, 43A85, 46J15]

Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]

32A36

Bergman空间

Bergman spaces

32A37

全纯函数的其它空间(例如: 有界平均振荡(BMOA), 消没平均振荡(VMOA))[参见46Exx]

Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]

32A38

全纯函数的代数[参见30H05, 46J10, 46J15]

Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]

32A40

全纯函数的边界特性

Boundary behavior of holomorphic functions

32A45

超函数[参见46F15]

Hyperfunctions [See also 46F15]

32A50

多复变量的调和分析[主要见43-XX]

Harmonic analysis of several complex variables [See mainly 43-XX]

32A55

奇异积分

Singular integrals

32A60

全纯函数的零点集

Zero sets of holomorphic functions

32A65

Banach代数方法[主要见46Jxx]

Banach algebra techniques [See mainly 46Jxx]

32A70

泛函分析方法[主要见46Exx]

Functional analysis techniques [See mainly 46Exx]

32A99

其它

None of the above, but in this section

32Bxx

局部解析几何[参见13-XX, 14-XX]

Local analytic geometry [See also 13-XX and 14-XX]

32B05

解析代数及其推广, 预备定理

Analytic algebras and generalizations, preparation theorems

32B10

解析集的芽, 局部参数化

Germs of analytic sets, local parametrization

32B15

仿射空间的解析子集

Analytic subsets of affine space

32B20

半解析集与子解析集[参见14P15]

Semi-analytic sets and subanalytic sets [See also 14P15]

32B25

三角剖分与有关问题

Triangulation and related questions

32B99

其它

None of the above, but in this section

32Cxx

解析空间

Analytic spaces

32C05

实解析流形, 实解析空间[参见14Pxx, 58A07]

Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]

32C07

实解析集, Nash函数[参见14P15, 14P20]

Real-analytic sets, complex Nash functions [See also 14P15, 14P20]

32C09

实解析流形的嵌入

Embedding of real analytic manifolds

32C11

复超几何[参见14A22, 14M30, 58A50]

Complex supergeometry [See also 14A22, 14M30, 58A50]

32C15

复空间

Complex spaces

32C18

解析空间的拓扑

Topology of analytic spaces

32C20

正规解析空间

Normal analytic spaces

32C22

解析空间的嵌入

Embedding of analytic spaces

32C25

解析子集与子流形

Analytic subsets and submanifolds

32C30

解析集和解析空间上的积分法, (局部理论, 32A2532A27)

Integration on analytic sets and spaces, currents (For local theory, see 32A25 or 32A27)

32C35

解析层和上同调群[参见14Fxx, 18F20, 55N30]

Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]

32C36

解析空间的局部上同调

Local cohomology of analytic spaces

32C37

对偶定理

Duality theorems

32C38

微分算子的层及其模, D-[参见14F10, 16S32, 35A27, 58J15]

Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15]

32C55

复空间中Levi问题; 推广

The Levi problem in complex spaces; generalizations

32C81

应用于物理

Applications to physics

32C99

其它

None of the above, but in this section

32Dxx

解析延拓

Analytic continuation

32D05

全纯域

Domains of holomorphy

32D10

全纯包络

Envelopes of holomorphy

32D15

解析目标的延拓

Continuation of analytic objects

32D20

可去奇点

Removable singularities

32D26

Riemann

Riemann domains

32D99

其它

None of the above, but in this section

32Exx

全纯凸性

Holomorphic convexity

32E05

全纯凸复空间, 约化理论

Holomorphically convex complex spaces, reduction theory

32E10

Stein空间, Stein流形

Stein spaces, Stein manifolds

32E20

多项式凸性

Polynomial convexity

32E30

全纯与多项式逼近, Runge, 插值()

Holomorphic and polynomial approximation, Runge pairs, interpolation

32E35

全纯函数的整体边界特性

Global boundary behavior of holomorphic functions

32E40

Levi问题

The Levi problem

32E99

其它

None of the above, but in this sect

32Fxx

几何凸性

Geometric convexity

32F10

q-凸性, q-凹性

q-convexity, q-concavity

32F17

其它凸性概念

Other notions of convexity

32F18

有限型条件

Finite-type conditions

32F27

几何凸性的拓扑推论

Topological consequences of geometric convexity

32F32

几何凸性的解析推论(消没定理等)

Analytical consequences of geometric convexity (vanishing theorems, etc.)

32F45

不变度量及其伪距离

Invariant metrics and pseudodistances

32F99

其它

None of the above, but in this section

32Gxx

解析结构的形变

Deformations of analytic structures

32G05

复结构的形变[参见13D10, 16S80, 58H10, 58H15]

Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]

32G07

特殊(例如: CR)结构的形变

Deformations of special (e.g. CR) structures

32G08

纤维丛的形变

Deformations of fiber bundles

32G10

子流形与子空间的形变

Deformations of submanifolds and subspaces

32G13

解析模问题(代数模问题, 14D20, 14D22, 14H10, 14J10)[参见14H15, 14J15]

Analytic moduli problems (For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10) [See also 14H15, 14J15]

32G15

Riemann曲面的模, Teichmüller理论[参见14H15, 30Fxx]

Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]

32G20

周期矩阵, Hodge结构的变分; 退化[参见14D05, 14D07, 14K30]

Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]

32G34

常微分方程的模与形变(例如: Knizhnik-Zamolodchikov方程)[参见34Mxx]

Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) [See also 34Mxx]

32G81

应用于物理

Applications to physics

32G99

其它

None of the above, but in this section

32Hxx

全纯映射与对应

Holomorphic mappings and correspondences

32H02

全纯映射, (全纯)嵌入及其相关问题

Holomorphic mappings, (holomorphic) embeddings and related questions

32H04

亚纯映射

Meromorphic mappings

32H12

边界映射的唯一性

Boundary uniqueness of mappings

32H25

Picard型定理及其推广(函数理论性质, 32A22)

Picard-type theorems and generalizations (For function-theoretic properties, see 32A22)

32H30

高维值分布理论(函数理论性质, 32A22)

Value distribution theory in higher dimensions (For function-theoretic properties, see 32A22)

32H35

真映射, 有限性定理

Proper mappings, finiteness theorems

32H40

映射的边界正则性

Boundary regularity of mappings

32H50

迭代问题

Iteration problems

32H99

其它

None of the above, but in this section

32Jxx

紧解析空间(Riemann曲面, 14Hxx, 30Fxx; 代数理论, 14Jxx)

Compact analytic spaces (For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx)

32J05

解析空间的紧化

Compactification of analytic spaces

32J10

代数相关定理

Algebraic dependence theorems

32J15

紧曲面

Compact surfaces

32J17

3

Compact 3-folds

32J18

n

Compact n-folds

32J25

代数几何的超越方法[参见14C30]

Transcendental methods of algebraic geometry [See also 14C30]

32J27

Kähler流形: 推广, 分类

Compact Kähler manifolds: generalizations, classification

32J81

应用于物理

Applications to physics

32J99

其它

None of the above, but in this section

32Kxx

解析空间的推广(还应在32-XX中至少指定一个分类号)

Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)

32K05

Banach解析空间[参见58Bxx]

Banach analytic spaces [See also 58Bxx]

32K07

形式与分次复空间[参见58C50]

Formal and graded complex spaces [See also 58C50]

32K15

解析空间上的可微函数, 可微空间[参见58C25]

Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]

32K99

其它

None of the above, but in this section

32Lxx

全纯纤维空间[参见55Rxx]

Holomorphic fiber spaces [See also 55Rxx]

32L05

全纯丛及其推广

Holomorphic bundles and generalizations

32L10

全纯向量丛的截面层与截面上同调, 一般结果[参见14F05, 18F20, 55N30]

Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]

32L15

丛凸性[参见32F10]

Bundle convexity [See also 32F10]

32L20

消没定理

Vanishing theorems

32L25

扭子理论, 二重纤维化[参见53C28]

Twistor theory, double fibrations [See also 53C28]

32L81

应用于物理

Applications to physics

32L99

其它

None of the above, but in this section

32Mxx

有一个自同构群的复空间

Complex spaces with a group of automorphisms

32M05

Lie, 作用于复空间的自同构群[参见22E10]

Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]

32M10

齐次复流形[参见14M17, 57T15]

Homogeneous complex manifolds [See also 14M17, 57T15]

32M12

殆齐次流形和空间[参见14M17]

Almost homogeneous manifolds and spaces [See also 14M17]

32M15

Hermite对称空间, 有界对称域, Jordan代数[参见22E10, 22E40, 53C35, 57T15]

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]

32M17

Cn的自同构群和仿射流形

Automorphism groups of Cn and affine manifolds

32M25

复向量场

Complex vector fields

32M99

其它

None of the above, but in this section

32Nxx

自守函数[参见11Fxx, 20H10, 22E40, 30F35]

Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]

32N05

多复变量自守函数的一般理论

General theory of automorphic functions of several complex variables

32N10

自守型

Automorphic forms

32N15

对称域中的自守函数

Automorphic functions in symmetric domains

32N99

其它

None of the above, but in this section

32Pxx

Archimedes分析(应在描述该问题的32-XX中至少指定一个其它分类号)

Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)

32P05

Archimedes分析(应在描述该问题的32-XX中至少指定一个其它分类号)

Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)

32P99

其它

None of the above, but in this section

32Qxx

复流形

Complex manifolds

32Q05

负曲率流形

Negative curvature manifolds

32Q10

正曲率流形

Positive curvature manifolds

32Q15

Kähler流形

Kähler manifolds

32Q20

Kähler-Einstein流形[参见53Cxx]

Kähler-Einstein manifolds [See also 53Cxx]

32Q25

Calabi-Yau理论[参见14J32]

Calabi-Yau theory [See also 14J30]

32Q26

稳定性概念

Notions of stability

32Q28

Stein流形

Stein manifolds

32Q30

单值化

Uniformization

32Q35

作为Euclid空间子域的复流形

Complex manifolds as subdomains of Euclidean space

32Q40

嵌入定理

Embedding theorems

32Q45

双曲和Kobayashi双曲流形

Hyperbolic and Kobayashi hyperbolic manifolds

32Q55

复流形的拓扑方面

Topological aspects of complex manifolds

32Q57

分类定理

Classification theorems

32Q60

殆复流形

Almost complex manifolds

32Q65

伪全纯曲线

Pseudoholomorphic curves

32Q99

其它

None of the above, but in this section

32Sxx

奇异性[参见58Kxx]

Singularities [See also 58Kxx]

32S05

局部奇异性[参见14J17]

Local singularities [See also 14J17]

32S10

解析局部环的不变量

Invariants of analytic local rings

32S15

等奇异性(拓扑的与解析的)[参见14E15]

Equisingularity (topological and analytic) [See also 14E15]

32S20

奇异性的整体理论; 上同调性质[参见14E15]

Global theory of singularities; cohomological properties [See also 14E15]

32S22

与超平面排列的关系[参见52C35]

Relations with arrangements of hyperplanes [See also 52C35]

32S25

曲面和超曲面的奇异性[参见14J17]

Surface and hypersurface singularities [See also 14J17]

32S30

奇异性的形变; 消没周期[参见14B07]

Deformations of singularities; vanishing cycles [See also 14B07]

32S35

奇异簇的混合Hodge理论[参见14C30, 14D07]

Mixed Hodge theory of singular variety [See also 14C30, 14D07]

32S40

单值(); 与微分方程及D-模的关系

Monodromy; relations with differential equations and D-modules

32S45

修正; 奇异性的分解[参见14E15]

Modifications; resolution of singularities [See also 14E15]

32S50

拓扑方面: Lefschetz定理, 拓扑分类, 不变量

Topological aspects: Lefschetz theorems, topological classification, invariants

32S55

Milnor纤维化; 与纽结理论的关系[参见57M25, 57Q45]

Milnor fibration; relations with knot theory [See also 57M25, 57Q45]

32S60

分层; 可构成层; 相交上同调[参见58Kxx]

Stratifications; constructible sheaves; intersection coho­mology [See also 58Kxx]

32S65

全纯向量场和叶状结构的奇异性

Singularities of holomorphic vector fields and foliations

32S70

奇异性的其它运算

Other operations on singularities

32S99

其它

None of the above, but in this section

32Txx

伪凸域

Pseudoconvex domains

32T05

正则域

Domains of holomorphy

32T15

强伪凸域

Strongly pseudoconvex domains

32T20

Worm

Worm domains

32T25

有限型域

Finite type domains

32T27

弱伪凸边界上几何及其解析不变量

Geometric and analytic invariants on weakly pseudo­convex boundaries

32T35

穷举函数

Exhaustion functions

32T40

峰函数

Peak functions

32T99

其它

None of the above, but in this section

32Uxx

多重位势论

Pluripotential theory

32U05

多重次调和函数及推广[参见31C10]

Plurisubharmonic functions and generalizations [See also 31C10]

32U10

多重次调和穷举函数

Plurisubharmonic exhaustion functions

32U15

一般多重位势论

General pluripotential theory

32U20

容量理论及其推广

Capacity theory and generalizations

32U25

Lelong

Lelong numbers

32U30

可去集

Removable sets

32U35

多重复Green函数

Pluricomplex Green functions

32U40

流动

Currents

32U99

其它

None of the above, but in this section

32Vxx

CR流形

CR manifolds

32V05

CR结构, CR算子, 及其推广

CR structures, CR operators, and generalizations

32V10

CR函数

CR functions

32V15

作为域边界的CR流形

CR manifolds as boundaries of domains

32V20

CR流形上的分析

Analysis on CR manifolds

32V25

函数的扩张及CR流形的其它解析对象

Extension of functions and other analytic objects from CR manifolds

32V30

CR流形的嵌入

Embeddings of CR manifolds

32V35

CR流形上的有限型条件

Finite type conditions on CR manifolds

32V40

复流形中的实子流形

Real submanifolds in complex manifolds

32V99

其它

None of the above, but in this section

32Wxx

多复变量微分算子

Differential operators in several complex variables

32W05

-Neumann算子

and -Neumann operators

32W10

bb-Neumann算子

b and b-Neumann operators

32W20

Monge-Ampère算子

Complex Monge-Ampère operators

32W25

多复变量中的伪微分算子

Pseudodifferential operators in several complex variables

32W30

多复变量中的热核

Heat kernels in several complex variables

32W50

复分析的其它偏微分方程

Other partial differential equations of complex analysis

32W99

其它

None of the above, but in this section

33-XX

特殊函数(33-XX研究函数的性质)(正交函数, 42Cxx; 组合方面, 05Axx; 数论方面, 11-XX; 表示理论, 22Exx)

Special functions (33-XX deals with the properties of functions as functions) (For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx)

33-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

33-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

33-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

33-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

33-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

33-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

33Bxx

初等经典函数

Elementary classical functions

33B10

指数函数与三角函数

Exponential and trigonometric functions

33B15

Γ函数, β函数与多Γ函数

Gamma, beta and polygamma functions

33B20

不完全的β函数与Γ函数(误差函数, 概率积分, Fresnel积分)

Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)

33B30

高阶对数函数

Higher logarithm functions

33B99

其它

None of the above, but in this section

33Cxx

超几何函数

Hypergeometric functions

33C05

经典超几何函数, 2F1

Classical hypergeometric functions, 2F1

33C10

Bessel函数与Airy函数, 柱函数, 0F1

Bessel and Airy functions, cylinder functions, 0F1

33C15

合流超几何函数, Whittaker函数, 1F1

Confluent hypergeometric functions, Whittaker functions, 1F1

33C20

广义超几何级数, pFq

Generalized hypergeometric series, pFq

33C45

超几何型的正交多项式和函数(JacobiLaguerreHermiteAskey格式等)[一般正交多项式和函数, 参见42C05]

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

33C47

其它特殊正交多项式和函数

Other special orthogonal polynomials and functions

33C50

可用单变量特殊函数表达的多变量正交多项式和函数

Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable

33C52

与根系相关的正交多项式和函数

Orthogonal polynomials and functions associated with root systems

33C55

球面调和函数

Spherical harmonics

33C60

由其(E, G, HI)定义的超几何积分和函数

Hypergeometric integrals and functions defined by them (E, G, H and I functions)

33C65

Appell, HornLauricella函数

Appell, Horn and Lauricella functions

33C67

与根系相关的超几何函数

Hypergeometric functions associated with root systems

33C70

多变量中的其它超几何函数和积分

Other hypergeometric functions and integrals in several variables

33C75

作为超几何函数的椭圆积分

Elliptic integrals as hypergeometric functions

33C80

与群和代数的关系, 及其有关课题

Connections with groups and algebras, and related topics

33C90

应用

Applications

33C99

其它

None of the above, but in this section

33Dxx

基本超几何函数

Basic hypergeometric functions

33D05

q函数, q函数与积分

q-gamma functions, q-beta functions and integrals

33D15

单变量中的基本超几何函数, rφs

Basic hypergeometric functions in one variable, rφs

33D45

基本正交多项式和函数(Askey-Wilson多项式等)

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

33D50

可用单变量基本超几何函数表达的多变量正交多项式和函数

Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable

33D52

与根系相关的基本正交多项式和函数(Macdonald多项式等)

Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)

33D60

基本超几何积分和由其定义的函数

Basic hypergeometric integrals and functions defined by them

33D65

双基本函数和多重基

Bibasic functions and multiple bases

33D67

与根系相关的基本超几何函数

Basic hypergeometric functions associated with root systems

33D70

多变量中的其它基本超几何函数和积分

Other basic hypergeometric functions and integrals in several variables

33D80

与量子群、Chevalley群、p-进群、Hecke代数及其相关课题的联系

Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics

33D90

应用

Applications

33D99

其它

None of the above, but in this section

33Exx

其它特殊函数

Other special functions

33E05

椭圆函数与积分

Elliptic functions and integrals

33E10

Lamé, Mathieu与球面波函数

Lamé, Mathieu, and spheroidal wave functions

33E12

Mittag-Leffer函数及其推广

Mittag-Leffler functions and generalizations

33E15

其它波函数

Other wave functions

33E17

Painlevé型函数

Painlevé-type functions

33E20

由级数和积分定义的其它函数

Other functions defined by series and integrals

33E30

来自微分、差分与积分方程的其它函数

Other functions coming from differential, difference and integral equations

33E50

特征p中的特殊函数(Γ函数等)

Special functions in characteristic p (gamma functions, etc.)

33E99

其它

None of the above, but in this section

33Fxx

计算方面

Computational aspects

33F05

数值逼近和赋值[参见65D20]

Numerical approximation and evaluation [See also 65D20]

33F10

符号计算(GosperZeilberger算法等)[参见68W30]

Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]

33F99

其它

None of the above, but in this section

34-XX

常微分方程

Ordinary differential equations

34-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

34-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

34-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

34-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

34-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

34-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

34Axx

一般理论

General theory

34A05

显式解和简化

Explicit solutions and reductions

34A07

模糊微分方程

Fuzzy differential equations

34A08

分式微分方程

Fractional differential equations

34A09

隐式方程, 微分-代数方程[参见65L80]

Implicit equations, differential-algebraic equations [See also 65L80]

34A12

解的初值问题、存在性、唯一性、连续依赖性及延拓

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

34A25

解析理论: 级数、变换、变换式、运算微积分等[参见44-XX]

Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]

34A26

微分方程中的几何方法

Geometric methods in differential equations

34A30

线性方程与方程组, 一般理论

Linear equations and systems, general

34A33

格微分方程

Lattice differential equations

34A34

非线性方程与方程组, 一般理论

Nonlinear equations and systems, general

34A35

无限阶微分方程

Differential equations of infinite order

34A36

不连续方程

Discontinuous equations

34A37

带有脉冲的微分方程

Differential equations with impulses

34A38

混合系统

Hybrid systems

34A40

微分不等式[参见26D20]

Differential inequalities [See also 26D20]

34A45

解的理论逼近(数值分析, 65Lxx)

Theoretical approximation of solutions (For numerical analysis, see 65Lxx)

34A55

逆问题

Inverse problems

34A60

微分包含[参见49J21, 49K21]

Differential inclusions [See also 49J21, 49K21]

34A99

其它

None of the above, but in this section

34Bxx

边值问题(常微分算子, 34Lxx)

Boundary value problems (For ordinary differential operators, see 34Lxx)

34B05

线性边值问题

Linear boundary value problems

34B07

具有非线性依赖谱参数的线性边值问题

Linear boundary value problems with nonlinear dependence on the spectral parameter

34B08

参数依赖的边值问题

Parameter dependent boundary value problems

34B09

边界特征值问题

Boundary eigenvalue problems

34B10

非局部和多点边值问题

Nonlocal and multipoint boundary value problems

34B15

非线性边值问题

Nonlinear boundary value problems

34B16

奇异非线性边值问题

Singular nonlinear boundary value problems

34B18

非线性边值问题的正解

Positive solutions of nonlinear boundary value problems

34B20

Weyl理论及其推广

Weyl theory and its generalizations

34B24

Sturm-Liouville理论[参见34Lxx]

Sturm-Liouville theory [See also 34Lxx]

34B27

Green函数

Green functions

34B30

特殊方程(MathieuHillBessel)

Special equations (Mathieu, Hill, Bessel, etc.)

34B37

带有脉冲的边值问题

Boundary value problems with impulses

34B40

无穷区间上的边值问题

Boundary value problems on infinite intervals

34B45

图和网络上的边值问题

Boundary value problems on graphs and networks

34B60

应用

Applications

34B99

其它

None of the above, but in this section

34Cxx

定性理论[参见37-XX]

Qualitative theory [See also 37-XX]

34C05

积分曲线的位置, 奇异点, 极限环

Location of integral curves, singular points, limit cycles

34C07

多项式和解析向量场的极限环理论(存在性, 唯一性, 边界, Hilbert16问题和分歧)

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications)

34C08

与实代数几何的联系(fewnomials、非奇异化、Abel积分零点等)

Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)

34C10

振荡理论, 零点, 不共轭性和比较理论

Oscillation theory, zeros, disconjugacy and comparison theory

34C11

增长性、有界性

Growth, boundedness

34C12

单调系统

Monotone systems

34C14

对称性, 不变量

Symmetries, invariants

34C15

非线性振荡, 耦合振子

Nonlinear oscillations, coupled oscillators

34C20

方程和方程组的变换和约化, 正规型

Transformation and reduction of equations and systems, normal forms

34C23

分歧[主要见37Gxx]

Bifurcation [See mainly 37Gxx]

34C25

周期解

Periodic solutions

34C26

松弛振荡

Relaxation oscillations

34C27

殆周期解和伪殆周期解

Almost and pseudoalmost periodic solutions

34C28

复性态, 混沌系统[参见37Dxx]

Complex behavior, chaotic systems [See also 37Dxx]

34C29

平均方法

Averaging method

34C37

同宿解和异宿解

Homoclinic and heteroclinic solutions

34C40

流形上的方程及系统

Equations and systems on manifolds

34C41

等价性, 渐近等价

Equivalence, asymptotic equivalence

34C45

不变流形

Invariant manifolds

34C46

多频系统

Multifrequency systems

34C55

滞后

Hysteresis

34C60

定性研究和模型仿真

Qualitative investigation and simulation of models

34C99

其它

None of the above, but in this section

34Dxx

稳定性理论[参见37C75, 93Dxx]

Stability theory [See also 37C75, 93Dxx]

34D05

渐近性质

Asymptotic properties

34D06

同步

Synchronization

34D08

特征和Liapunov指数

Characteristic and Lyapunov exponents

34D09

二分法, 三分法

Dichotomy, trichotomy

34D10

摄动

Perturbations

34D15

奇摄动

Singular perturbations

34D20

稳定性

Stability

34D23

全局稳定性

Global stability

34D30

结构稳定性与模拟概念[参见37C20]

Structural stability and analogous concepts [See also 37C20]

34D35

解流形的稳定性

Stability of manifolds of solutions

34D45

吸引子[参见37C30, 37D45]

Attractors [See also 37C70, 37D45]

34D99

其它

None of the above, but in this section

34Exx

渐近理论

Asymptotic theory

34E05

渐近展开

Asymptotic expansions

34E10

摄动, 渐近

Perturbations, asymptotics

34E13

多重尺度法

Multiple scale methods

34E15

奇摄动, 一般理论

Singular perturbations, general theory

34E17

鸭解

Canard solutions

34E18

非标准分析法

Methods of nonstandard analysis

34E20

奇摄动, 转向点理论, WKB方法

Singular perturbations, turning point theory, WKB methods

34E99

其它

None of the above, but in this section

34Fxx

随机性的方程与方程组[参见34K50, 60H10, 93E03]

Equations and systems with randomness [See also 34K50, 60H10, 93E03]

34F05

随机性的方程与方程组[参见34K50, 60H10, 93E03]

Equations and systems with randomness [See also 34K50, 60H10, 93E03]

34F10

分歧

Bifurcation

34F15

共振现象

Resonance phenomena

34F99

其它

None of the above, but in this section

34Gxx

抽象空间中的微分方程[参见34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]

Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]

34G10

线性方程[参见47D06, 47D09]

Linear equations [See also 47D06, 47D09]

34G20

非线性方程[参见47Hxx, 47Jxx]

Nonlinear equations [See also 47Hxx, 47Jxx]

34G25

发展包含

Evolution inclusions

34G99

其它

None of the above, but in this section

34Hxx

控制问题[参见49J15, 49K15, 93C15]

Control problems [See also 49J15, 49K15, 93C15]

34H05

控制问题[参见49J15, 49K15, 93C15]

Control problems [See also 49J15, 49K15, 93C15]

34H10

混沌控制

Chaos control

34H15

稳定化

Stabilization

34H20

分歧控制

Bifurcation control

34H99

其它

None of the above, but in this section

34Kxx

泛函-微分与微分-差分方程[参见37-XX]

Functional-differential and differential-diffe­rence equations [See also 37-XX]

34K05

一般理论

General theory

34K06

线性泛函-微分方程

Linear functional-differential equations

34K07

解的理论逼近

Theoretical approximation of solutions

34K08

泛函微分算子的谱理论

Spectral theory of functional-differential operators

34K09

泛函微分包含

Functional-differential inclusions

34K10

边值问题

Boundary value problems

34K11

振荡理论

Oscillation theory

34K12

解的增长性, 有界性, 比较

Growth, boundedness, comparison of solutions

34K13

周期解

Periodic solutions

34K14

殆周期解及伪周期解

Almost and pseudoperiodic solutions

34K17

方程和方程组的变换和简化, 标准型

Transformation and reduction of equations and systems, normal forms

34K18

分歧理论

Bifurcation theory

34K19

不变流形

Invariant manifolds

34K20

稳定性理论

Stability theory

34K21

稳态解

Stationary solutions

34K23

解的复(混沌)特性

Complex (chaotic) behavior of solutions

34K25

渐近理论

Asymptotic theory

34K26

奇摄动

Singular perturbations

34K27

摄动

Perturbations

34K28

解的数值逼近

Numerical approximation of solutions

34K29

逆问题

Inverse problems

34K30

抽象空间中的方程[参见34Gxx, 35R09, 35R10, 47Jxx]

Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]

34K31

格泛函微分方程

Lattice functional-differential equations

34K32

隐式方程

Implicit equations

34K33

平均

Averaging

34K34

混合系统

Hybrid systems

34K35

控制问题[参见49J21, 49K21, 93C23]

Control problems [See also 49J21, 49K21, 93C23]

34K36

模糊泛函微分方程

Fuzzy functional-differential equations

34K37

具有分数导数的泛函微分方程

Functional-differential equations with fractional derivatives

34K38

泛函微分不等式

Functional-differential inequalities

34K40

中立型方程

Neutral equations

34K45

具有脉冲的方程

Equations with impulses

34K50

随机泛函-微分方程[参见60Hxx]

Stochastic functional-differential equations [See also 60Hxx]

34K60

定性分析和模型仿真

Qualitative investigation and simulation of models

34K99

其它

None of the above, but in this section

34Lxx

常微分算子[参见47E05]

Ordinary differential operators [See also 47E05]

34L05

一般谱论

General spectral theory

34L10

特征函数, 特征函数展开, 特征函数的完备性

Eigenfunction, eigenfunction expansions, completeness of eigenfunctions

34L15

特征值, 特征值的估计, 上界与下界

Eigenvalues, estimation of eigenvalues, upper and lower bounds

34L16

特征值与谱的其它部分的数值逼近

Numerical approximation of eigenvalues and of other parts of the spectrum

34L20

特征值的渐近分布, 特征函数的渐近理论

Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions

34L25

散射理论, 逆散射

Scattering theory, inverse scattering

34L30

非线性常微分算子

Nonlinear ordinary differential operators

34L40

特殊算子(Dirac、一维Schrödin­ger)

Particular operators (Dirac, one-dimensional Schrödinger, etc.)

34L99

其它

None of the above, but in this section

34Mxx

复域中的微分方程[参见30Dxx, 32G34]

Differential equations in the complex domain [See also 30Dxx, 32G34]

34M03

线性方程和方程组

Linear equations and systems

34M05

整解和亚纯解

Entire and meromorphic solutions

34M10

解的振荡和增长

Oscillation, growth of solutions

34M15

代数方面(微分-代数, 超超越性, 群理论)

Algebraic aspects (differential-algebraic, hypertranscen­dence, group-theoretical)

34M25

形式解, 变换技巧

Formal solutions, transform techniques

34M30

渐近性, 求和法

Asymptotics, summation methods

34M35

解的奇异性、单值[]、局部性态, 标准型

Singularities, monodromy, local behavior of solutions, normal forms

34M40

Stokes现象和联络问题(线性和非线性)

Stokes phenomena and connection problems (linear and nonlinear)

34M45

复流形上的微分方程

Differential equations on complex manifolds

34M50

逆问题(Riemann-Hilbert、逆微分Galois)

Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)

34M55

Painlevé和其它特殊方程; 分类, 谱系

Painlevé and other special equations; classification, hierarchies

34M56

等单值形变

Isomonodromic deformations

34M60

复域中的奇摄动问题(WKB, 转向点, 最速下降)[参见34E20]

Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]

34M99

其它

None of the above, but in this section

34Nxx

时间尺度或测度链上的动力学方程(时间尺度上的实分析, 26E70)

Dynamic equations on time scales or measure chains (For real analysis on time scales see 26E70)

34N05

时间尺度或测度链上的动力学方程 (时间尺度上的实分析, 26E70)

Dynamic equations on time scales or measure chains (For real analysis on time scales, see 26E70)

34N99

其它

None of the above, but in this section

35-XX

偏微分方程

Partial differential equations

35-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

35-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

35-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

35-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

35-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

35-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

35Axx

一般课题

General topics

35A01

存在性问题: 全局存在性, 局部存在性, 不存在性

Existence problems: global existence, local existence, nonexistence

35A02

唯一性问题: 全局唯一性, 局部唯一性, 不唯一性

Uniqueness problems: global uniqueness, local unique­ness, nonuniqueness

35A08

基本解

Fundamental solutions

35A09

经典解

Classical solutions

35A10

Cauchy-Kovalevskaya定理

Cauchy-Kovalevskaya theorems

35A15

变分法

Variational methods

35A16

拓扑和单调性方法

Topological and monotonicity methods

35A17

参数的

Parametrices

35A18

波前集

Wave front sets

35A20

解析方法, 奇异性

Analytic methods, singularities

35A21

奇异性的传播

Propagation of singularities

35A22

变换方法(例如: 积分变换)

Transform methods (e.g. integral transforms)

35A23

涉及导数、微分及积分算子的不等式, 积分不等式

Inequalities involving derivatives and differential and integral operators, inequalities for integrals

35A24

常微分方程的方法

Methods of ordinary differential equations

35A25

其它特殊方法

Other special methods

35A27

微局部方法; 偏微分方程中同调代数与层理论方法[参见32C38, 58J15]

Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]

35A30

几何理论, 特征, 变换[参见58J70, 58J72]

Geometric theory, characteristics, transformations [See also 58J70, 58J72]

35A35

解的理论逼近(数值分析, 65Mxx, 65Nxx)

Theoretical approximation to solutions (For numerical analysis, see 65Mxx, 65Nxx)

35A99

其它

None of the above, but in this section

35Bxx

解的定性性质

Qualitative properties of solutions

35B05

振荡、解的零点、均值定理等

Oscillation, zeros of solutions, mean value theorems, etc.

35B06

对称、不变量等

Symmetries, invariants, etc.

35B07

轴对称解

Axially symmetric solutions

35B08

整解

Entire solutions

35B09

正解

Positive solutions

35B10

周期解

Periodic solutions

35B15

殆周期解及伪殆周期解

Almost and pseudo-almost periodic solutions

35B20

摄动

Perturbations

35B25

奇摄动

Singular perturbations

35B27

齐性化; 带有周期结构媒介中的方程[参见74Qxx, 76M50]

Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]

35B30

依赖于初始和边界数据、参数的解[参见37Cxx]

Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

35B32

分歧[参见37Gxx, 37K50]

Bifurcation [See also 37Gxx, 37K50]

35B33

临界指数

Critical exponents

35B34

共振

Resonances

35B35

稳定性

Stability

35B36

模式形成

Pattern formation

35B38

临界点

Critical points

35B40

解的渐近特性

Asymptotic behavior of solutions

35B41

吸引子

Attractors

35B42

惯性流形

Inertial manifolds

35B44

爆破

Blow-up

35B45

先验估计

A priori estimates

35B50

极大值原理

Maximum principles

35B51

比较原理

Comparison principles

35B53

Liouville定理, Phragmén-Lin­delöf定理

Liouville theorems, Phragmén-Lindelöf theorems

35B60

解的连续与延拓[参见58A15, 58A17, 58Hxx]

Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]

35B65

解的光滑性和正则性

Smoothness and regularity of solutions

35B99

其它

None of the above, but in this section

35Cxx

解的表示

Representations of solutions

35C05

闭型解

Solutions in closed form

35C06

自相似解

Self-similar solutions

35C07

行波解

Traveling wave solutions

35C08

孤子解

Soliton solutions

35C09

三角解

Trigonometric solutions

35C10

级数解

Series solutions

35C11

多项式解

Polynomial solutions

35C15

解的积分表示

Integral representations of solutions

35C20

渐近展开

Asymptotic expansions

35C99

其它

None of the above, but in this section

35Dxx

广义解

Generalized solutions

35D30

弱解

Weak solutions

35D35

强解

Strong solutions

35D40

粘性解

Viscosity solutions

35D99

其它

None of the above, but in this section

35Exx

带常系数的方程与方程组[参见35N05]

Equations and systems with constant coefficients [See also 35N05]

35E05

基本解

Fundamental solutions

35E10

凸性性质

Convexity properties

35E15

初值问题

Initial value problems

35E20

一般理论

General theory

35E99

其它

None of the above, but in this section

35Fxx

一般一阶方程与方程组

General first-order equations and systems

35F05

一阶线性方程

Linear first-order equations

35F10

一阶线性方程的初值问题

Initial value problems for linear first-order equations

35F15

一阶线性方程的边值问题

Boundary value problems for linear first-order equations

35F16

一阶线性方程的初-边值问题

Initial-boundary value problems for linear first-order equations

35F20

一阶非线性方程

Nonlinear first-order equations

35F21

Hamilton-Jacobi方程

Hamilton-Jacobi equations

35F25

一阶非线性方程的初值问题

Initial value problems for nonlinear first-order equations

35F30

一阶非线性方程的边值问题

Boundary value problems for nonlinear first-order equations

35F31

一阶非线性方程的初-边值问题

Initial-boundary value problems for nonlinear first-order equations

35F35

一阶线性方程组

Linear first-order systems

35F40

一阶线性方程组的初值问题

Initial value problems for linear first-order systems

35F45

一阶线性方程组的边值问题

Boundary value problems for linear first-order systems

35F46

一阶线性方程组的初-边值问题

Initial-boundary value problems for linear first-order systems

35F50

一阶非线性方程组

Nonlinear first-order systems

35F55

一阶非线性方程组的初值问题

Initial value problems for nonlinear first-order systems

35F60

一阶非线性方程组的边值问题

Boundary value problems for nonlinear first-order systems

35F61

一阶非线性方程组的初-边值问题

Initial-boundary value problems for nonlinear first-order systems

35F99

其它

None of the above, but in this section

35Gxx

一般高阶方程与方程组

General higher-order equations and systems

35G05

高阶线性方程

Linear higher-order equations

35G10

高阶线性方程的初值问题

Initial value problems for linear higher-order equations

35G15

高阶线性方程的边值问题

Boundary value problems for linear higher-order equations

35G16

高阶线性方程的初-边值问题

Initial-boundary value problems for linear higher-order equations

35G20

高阶非线性方程

Nonlinear higher-order equations

35G25

高阶非线性方程的初值问题

Initial value problems for nonlinear higher-order equations

35G30

高阶非线性方程的边值问题

Boundary value problems for nonlinear higher-order equations

35G31

高阶非线性方程的初-边值问题

Initial-boundary value problems for nonlinear higher-order equations

35G35

高阶线性方程组

Linear higher-order systems

35G40

高阶线性方程组的初值问题

Initial value problems for linear higher-order systems

35G45

高阶线性方程组的边值问题

Boundary value problems for linear higher-order systems

35G46

高阶线性方程组的初-边值问题

Initial-boundary value problems for linear higher-order systems

35G50

高阶非线性方程组

Nonlinear higher-order systems

35G55

高阶非线性方程组的初值问题

Initial value problems for nonlinear higher-order systems

35G60

高阶非线性方程组的边值问题

Boundary value problems for nonlinear higher-order systems

35G61

高阶非线性方程组的初-边值问题

Initial-boundary value problems for nonlinear higher-order systems

35G99

其它

None of the above, but in this section

35Hxx

封闭-椭圆型方程与方程组

Close-to-elliptic equations and systems

35H10

超椭圆型方程

Hypoelliptic equations

35H20

次椭圆型方程

Subelliptic equations

35H30

拟椭圆型方程

Quasi-elliptic equations

35H99

其它

None of the above, but in this section

35Jxx

椭圆型方程和方程组[参见58J10, 58J20]

Elliptic equations and systems [See also 58J10, 58J20]

35J05

Laplace方程, 约化波动方程(Helmholtz方程), Poisson方程[参见31Axx, 31Bxx]

Laplace equation, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]

35J08

Green函数

Green’s functions

35J10

Schrödinger算子[参见35Pxx]

Schrödinger operator [See also 35Pxx]

35J15

二阶椭圆型方程

Second-order elliptic equations

35J20

二阶椭圆型方程的变分法

Variational methods for second-order elliptic equations

35J25

二阶椭圆型方程的边值问题

Boundary value problems for second-order elliptic equations

35J30

高阶椭圆型方程[参见31A30, 31B30]

Higher-order elliptic equations [See also 31A30, 31B30]

35J35

高阶椭圆型方程的变分法

Variational methods for higher-order elliptic equations

35J40

高阶椭圆型方程的边值问题

Boundary value problems for higher-order elliptic equations

35J46

一阶椭圆型方程组

First-order elliptic systems

35J47

二阶椭圆型方程组

Second-order elliptic systems

35J48

高阶椭圆型方程组

Higher-order elliptic systems

35J50

椭圆型方程组的变分法

Variational methods for elliptic systems

35J56

一阶椭圆型方程组的边值问题

Boundary value problems for first-order elliptic systems

35J57

二阶椭圆型方程组的边值问题

Boundary value problems for second-order elliptic systems

35J58

高阶椭圆型方程组的边值问题

Boundary value problems for higher-order elliptic systems

35J60

非线性椭圆型方程

Nonlinear elliptic equations

35J61

半线性椭圆型方程

Semilinear elliptic equations

35J62

拟线性椭圆型方程

Quasilinear elliptic equations

35J65

线性椭圆型方程的非线性边值问题

Nonlinear boundary value problems for linear elliptic equations

35J66

非线性椭圆型方程的非线性边值问题

Nonlinear boundary value problems for nonlinear elliptic equations

35J67

椭圆型方程解的边值问题

Boundary values of solutions to elliptic equations

35J70

退化椭圆型方程

Degenerate elliptic equations

35J75

奇异椭圆型方程

Singular elliptic equations

35J86

线性椭圆型单侧问题和线性椭圆型变分不等式[参见35R35, 49J40]

Linear elliptic unilateral problems and linear elliptic variational inequalities [See also 35R35, 49J40]

35J87

非线性椭圆型单侧问题和非线性椭圆型变分不等式[参见35R35, 49J40]

Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40]

35J88

椭圆型变分不等式系统[参见35R35, 49J40]

Systems of elliptic variational inequalities [See also 35R35, 49J40]

35J91

具有Laplace, -Laplace或多-Laplace算子的半线性椭圆型方程

Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian

35J92

具有p-Laplace算子的拟线性椭圆型方程

Quasilinear elliptic equations with p-Laplacian

35J93

具有平均曲率算子的拟线性椭圆型方程

Quasilinear elliptic equations with mean curvature operator

35J96

椭圆型Monge-Ampére方程

Elliptic Monge-Ampére equations

35J99

其它

None of the above, but in this section

35Kxx

抛物型方程与方程组[参见35Bxx, 35Dxx, 35R30, 35R35, 58J35]

Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]

35K05

热方程

Heat equation

35K08

热核

Heat kernel

35K10

二阶抛物型方程

Second-order parabolic equations

35K15

二阶抛物型方程的初值问题

Initial value problems for second-order parabolic equations

35K20

二阶抛物型方程的初-边值问题

Initial-boundary value problems for second-order parabolic equations

35K25

高阶抛物型方程

Higher-order parabolic equations

35K30

高阶抛物型方程的初值问题

Initial value problems for higher-order parabolic equations

35K35

高阶抛物型方程的初-边值问题

Initial-boundary value problems for higher-order parabolic equations

35K40

二阶抛物型方程组

Second-order parabolic systems

35K41

高阶抛物型方程组

Higher-order parabolic systems

35K45

二阶抛物型方程组的初值问题

Initial value problems for second-order parabolic systems

35K46

高阶抛物型方程组的初值问题

Initial value problems for higher-order parabolic systems

35K51

二阶抛物型方程组的初-边值问题

Initial-boundary value problems for second-order parabolic systems

35K52

高阶抛物型方程组的初-边值问题

Initial-boundary value problems for higher-order parabolic systems

35K55

非线性抛物型方程

Nonlinear parabolic equations

35K57

反应-扩散方程

Reaction-diffusion equations

35K58

半线性抛物型方程

Semilinear parabolic equations

35K59

拟线性抛物型方程

Quasilinear parabolic equations

35K60

线性抛物型方程的非线性初值问题

Nonlinear initial value problems for linear parabolic equations

35K61

非线性抛物型方程的非线性初-边值问题

Nonlinear initial-boundary value problems for nonlinear parabolic equations

35K65

退化抛物型方程

Degenerate parabolic equations

35K67

奇异抛物型方程

Singular parabolic equations

35K70

超抛物型方程、伪抛物型方程等

Ultraparabolic equations, pseudoparabolic equations, etc.

35K85

线性抛物型单侧问题和线性抛物型变分不等式[参见35R35, 49J40]

Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]

35K86

非线性抛物型单侧问题和非线性抛物型变分不等式[参见35R35, 49J40]

Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40]

35K87

抛物型变分不等式系统[参见35R35, 49J40]

Systems of parabolic variational inequalities [See also 35R35, 49J40]

35K90

抽象抛物型方程

Abstract parabolic equations

35K91

具有Laplace、双-Laplace或多-Laplace算子的半线性抛物型方程

Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian

35K92

具有p-Laplace算子的拟线性抛物型方程

Quasilinear parabolic equations with p-Laplacian

35K93

具有平均曲率算子的拟线性抛物型方程

Quasilinear parabolic equations with mean curvature operator

35K96

抛物型Monge-Ampére方程

Parabolic Monge-Ampére equations

35K99

其它

None of the above, but in this section

35Lxx

双曲型方程和方程组[参见58J45]

Hyperbolic equations and systems [See also 58J45]

35L02

一阶双曲型方程

First-order hyperbolic equations

35L03

一阶双曲型方程的初值问题

Initial value problems for first-order hyperbolic equations

35L04

一阶双曲型方程的初-边值问题

Initial-boundary value problems for first-order hyperbolic equations

35L05

波动方程

Wave equation

35L10

二阶双曲型方程

Second-order hyperbolic equations

35L15

二阶双曲型方程的初值问题

Initial value problems for second-order hyperbolic equa­tions

35L20

二阶双曲型方程的初-边值问题

Initial-boundary value problems for second-order hyper­bolic equations

35L25

高阶双曲型方程

Higher-order hyperbolic equations

35L30

高阶双曲型方程的初值问题

Initial value problems for higher-order hyperbolic equa­tions

35L35

高阶双曲型方程的初-边值问题

Initial-boundary value problems for higher-order hyper­bolic equations

35L40

一阶双曲型方程组

First-order hyperbolic systems

35L45

一阶双曲型方程组的初值问题

Initial value problems for first-order hyperbolic systems

35L50

一阶双曲型方程组的初-边值问题

Initial-boundary value problems for first-order hyperbolic systems

35L51

二阶双曲型方程组

Second-order hyperbolic systems

35L52

二阶双曲型方程组的初值问题

Initial value problems for second-order hyperbolic systems

35L53

二阶双曲型方程组的初-边值问题

Initial-boundary value problems for second-order hyperbolic systems

35L55

高阶双曲型方程组

Higher-order hyperbolic systems

35L56

高阶双曲型方程组的初值问题

Initial value problems for higher-order hyperbolic systems

35L57

高阶双曲型方程组的初-边值问题

Initial-boundary value problems for higher-order hyperbolic systems

35L60

一阶非线性双曲型方程

Nonlinear first-order hyperbolic equations

35L65

守恒律

Conservation laws

35L67

激波和奇异性[参见58Kxx, 76L05]

Shocks and singularities [See also 58Kxx, 76L05]

35L70

二阶非线性双曲型方程

Nonlinear second-order hyperbolic equations

35L71

二阶半线性双曲型方程

Semilinear second-order hyperbolic equations

35L72

二阶拟线性双曲型方程

Quasilinear second-order hyperbolic equations

35L75

高阶非线性双曲型方程

Nonlinear higher-order hyperbolic equations

35L76

高阶半线性双曲型方程

Semilinear higher-order hyperbolic equations

35L77

高阶拟线性双曲型方程

Quasilinear higher-order hyperbolic equations

35L80

退化双曲型方程

Degenerate hyperbolic equations

35L81

奇异双曲型方程

Singular hyperbolic equations

35L82

伪双曲型方程

Pseudohyperbolic equations

35L85

线性双曲型单侧问题和线性双曲型变分不等式[参见35R35, 49J40]

Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]

35L86

非线性双曲型单侧问题和非线性双曲型变分不等式[参见35R35, 49J40]

Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]

35L87

双曲型方程组的单侧问题和变分不等式[参见35R35, 49J40]

Unilateral problems and variational inequalities for hyperbolic systems [See also 35R35, 49J40]

35L90

抽象双曲型方程

Abstract hyperbolic equations

35L99

其它

None of the above, but in this section

35Mxx

特殊类型的方程和方程组(混合、复合等)

Equations and systems of special type (mixed, composite, etc.)

35M10

混合型方程

Equations of mixed type

35M11

混合型方程的初值问题

Initial value problems for equations of mixed type

35M12

混合型方程的边值问题

Boundary value problems for equations of mixed type

35M13

混合型方程的初-边值问题

Initial-boundary value problems for equations of mixed type

35M30

混合型方程组

Systems of mixed type

35M31

混合型方程组的初值问题

Initial value problems for systems of mixed type

35M32

混合型方程组的边值问题

Boundary value problems for systems of mixed type

35M33

混合型方程组的初-边值问题

Initial-boundary value problems for systems of mixed type

35M85

混合型线性单侧问题和变分不等式[参见35R35, 49J40]

Linear unilateral problems and variational inequalities of mixed type [See also 35R35, 49J40]

35M86

混合型非线性单侧问题和非线性变分不等式[参见35R35, 49J40]

Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also 35R35, 49J40]

35M87

混合型变分不等式系统[参见35R35, 49J40]

Systems of variational inequalities of mixed type [See also 35R35, 49J40]

35M99

其它

None of the above, but in this section

35Nxx

超定组[参见58Hxx, 58J10, 58J15]

Overdetermined systems [See also 58Hxx, 58J10, 58J15]

35N05

常系数超定组

Overdetermined systems with constant coefficients

35N10

变系数超定组

Overdetermined systems with variable coefficients

35N15

-Neumann问题及推广; 形式复形[参见32W05, 32W10, 58J10]

-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]

35N20

超定初值问题

Overdetermined initial value problems

35N25

超定边值问题

Overdetermined boundary value problems

35N30

超定初-边值问题

Overdetermined initial-boundary value problems

35N99

其它

None of the above, but in this section

35Pxx

谱理论与特征值问题[参见47Axx, 47Bxx, 47F05]

Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05]

35P05

线性谱理论中的一般课题

General topics in linear spectral theory

35P10

特征函数的完备性, 特征函数展开

Completeness of eigenfunctions, eigenfunction expansions

35P15

特征值的估计, 上界与下界

Estimation of eigenvalues, upper and lower bounds

35P20

特征值与特征函数的渐近分布

Asymptotic distribution of eigenvalues and eigenfunctions

35P25

散射理论[参见47A40]

Scattering theory [See also 47A40]

35P30

非线性特征值问题, 非线性谱理论

Nonlinear eigenvalue problems, nonlinear spectral theory

35P99

其它

None of the above, but in this section

35Qxx

数理方程及在其它领域的应用[参见35J05, 35J10, 35K05, 35L05]

Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]

35Q05

Euler-Poisson-Darboux方程

Euler-Poisson-Darboux equations

35Q15

Riemann-Hilbert问题[参见30E25, 31A25, 31B20]

Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]

35Q20

Boltzmann方程

Boltzmann equations

35Q30

Navier-Stokes方程[参见76D05, 76D07, 76N10]

Navier-Stokes equations [See also 76D05, 76D07, 76N10]

35Q31

Euler方程[参见76D05, 76D07, 76N10]

Euler equations [See also 76D05, 76D07, 76N10]

35Q35

与流体力学有关的偏微分方程

PDEs in connection with fluid mechanics

35Q40

与量子力学有关的偏微分方程

PDEs in connection with quantum mechanics

35Q41

时间依赖的Schrödinger方程, Dirac方程

Time-dependent Schrödinger equations, Dirac equations

35Q51

类孤子方程[参见 37K40]

Soliton-like equations [See also 37K40]

35Q53

KdV方程 (Korteweg-de Vries)[参见37K10]

KdV-like equations (Korteweg-de Vries) [See also 37K10]

35Q55

NLS方程(非线性Schrö­dinger)[参见37K10]

NLS-like equations (nonlinear Schrödinger) [See also 37K10]

35Q56

Ginzburg-Landau方程

Ginzburg-Landau equations

35Q60

与光学和电磁理论有关的偏微分方程

PDEs in connection with optics and electromagnetic theory

35Q61

Maxwell方程

Maxwell equations

35Q62

与统计学有关的偏微分方程

PDEs in connection with statistics

35Q68

与计算机科学有关的偏微分方程

PDEs in connection with computer science

35Q70

与粒子及系统力学有关的偏微分方程

PDEs in connection with mechanics of particles and systems

35Q74

与变形固体力学有关的偏微分方程

PDEs in connection with mechanics of deformable solids

35Q75

与相对论和重力理论有关的偏微分方程

PDEs in connection with relativity and gravitational theory

35Q76

Einstein方程

Einstein equations

35Q80

与经典热力学及热传导有关的偏微分方程

PDEs in connection with classical thermodynamics and heat transfer

35Q82

与统计力学有关的偏微分方程

PDEs in connection with statistical mechanics

35Q83

Vlasov方程

Vlasov-like equations

35Q84

Fokker-Planck方程

Fokker-Planck equations

35Q85

与天文学及天体物理学有关的偏微分方程

PDEs in connection with astronomy and astrophysics

35Q86

与地球物理学有关的偏微分方程

PDEs in connection with geophysics

35Q90

与数学规划有关的偏微分方程

PDEs in connection with mathematical programming

35Q91

与博弈论, 经济学, 社会学及行为科学有关的偏微分方程

PDEs in connection with game theory, economics, social and behavioral sciences

35Q92

与生物学及其它自然科学有关的偏微分方程

PDEs in connection with biology and other natural sciences

35Q93

与控制和最优化有关的偏微分方程

PDEs in connection with control and optimization

35Q94

与信息和通信有关的偏微分方程

PDEs in connection with information and communication

35Q99

其它

None of the above, but in this section

35Rxx

杂题(流形上的方程, 58Jxx; 解的流形, 58Bxx; 随机偏微分方程, 参见60H15)

Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see also 60H15)

35R01

流形上的偏微分方程[参见32Wxx, 53Cxx, 58Jxx]

Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx]

35R02

图和网络(分支或多边形空间)上的偏微分方程

Partial differential equations on graphs and networks (ramified or polygonal spaces)

35R03

Heisenberg群、Lie群、Carnot群等群上的偏微分方程

Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.

35R05

带有间断系数或数据的偏微分方程

Partial differential equations with discontinuous coefficients or data

35R06

带测度的偏微分方程

Partial differential equations with measure

35R09

积分-偏微分方程[参见45Kxx]

Integro-partial differential equations [See also 45Kxx]

35R10

偏泛函-微分方程

Partial functional-differential equations

35R11

分数偏微分方程

Fractional partial differential equations

35R12

脉冲偏微分方程

Impulsive partial differential equations

35R13

模糊偏微分方程

Fuzzy partial differential equations

35R15

无限维(例如: 函数)空间上的偏微分方程(=无穷多变量的偏微分方程)[参见46Gxx, 58D25]

Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]

35R20

偏算子-微分方程(例如: 抽象空间赋值函数有限维空间的偏微分方程)[参见34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]

Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]

35R25

不适定问题

Improperly posed problems

35R30

逆问题

Inverse problems

35R35

自由边界问题

Free boundary problems

35R37

运动边界问题

Moving boundary problems

35R45

偏微分不等式

Partial differential inequalities

35R50

无限阶的偏微分方程

Partial differential equations of infinite order

35R60

具有随机性的偏微分方程, 随机偏微分方程[参见60H15]

Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

35R70

多值右边的偏微分方程

Partial differential equations with multivalued right-hand sides

35R99

其它

None of the above, but in this section

35Sxx

伪微分算子与偏微分算子的其它推广[参见47G30, 58J40]

Pseudodifferential operators and other genera­lizations of partial differential operators [See also 47G30, 58J40]

35S05

伪微分算子

Pseudodifferential operators

35S10

伪微分算子的初值问题

Initial value problems for pseudodifferential operators

35S11

伪微分算子的初-边值问题

Initial-boundary value problems for pseudodifferential operators

35S15

伪微分算子的边值问题

Boundary value problems for pseudodifferential operators

35S30

Fourier积分算子

Fourier integral operators

35S35

拓扑方面: 相交上同调、分层集等[参见32C38, 32S40, 32S60, 58J15]

Topological aspects: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]

35S50

仿微分算子

Paradifferential operators

35S99

其它

None of the above, but in this section

37-XX

动力系统和遍历理论[参见26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]

Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]

37-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

37-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

37-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

37-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

37-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

37-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

37Axx

遍历理论[参见28Dxx]

Ergodic theory [See also 28Dxx]

37A05

保测变换

Measure-preserving transformations

37A10

保测变换的单参数连续族

One-parameter continuous families of measure-preserving transformations

37A15

保测变换的一般群[主要见22Fxx]

General groups of measure-preserving transformations [See mainly 22Fxx]

37A17

齐次流[参见22Fxx]

Homogeneous flows [See also 22Fxx]

37A20

轨道等价性, 余圈, 遍历等价关系

Orbit equivalence, cocycles, ergodic equivalence relations

37A25

遍历性, 混合, 混合速率

Ergodicity, mixing, rates of mixing

37A30

遍历定理, 谱论, Markov算子(算子遍历理论, 主要见47A35)

Ergodic theorems, spectral theory, Markov operators (For operator ergodic theory, see mainly 47A35)

37A35

熵和其它不变量, 同构, 分类

Entropy and other invariants, isomorphism, classification

37A40

非奇异(和无穷保测)变换

Nonsingular (and infinite-measure preserving) transformations

37A45

与数论和调和分析的关系[参见11Kxx]

Relations with number theory and harmonic analysis [See also 11Kxx]

37A50

与概率论和随机过程的关系[参见60Fxx60G10]

Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]

37A55

C*-代数理论的关系[主要见46L55]

Relations with the theory of C*-algebras [See mainly 46L55]

37A60

统计力学中的动力系统[参见82Cxx]

Dynamical systems in statistical mechanics [See also 82Cxx]

37A99

其它

None of the above, but in this section

37Bxx

拓扑动力学[参见54H20]

Topological dynamics [See also 54H20]

37B05

具有特殊性质的变换和群作用(极小性、远离、邻近等)

Transformations and group actions with special properties (minimality, distality, proximality, etc.)

37B10

符号动力学[参见37Cxx, 37Dxx]

Symbolic dynamics [See also 37Cxx, 37Dxx]

37B15

细胞自动机[参见68Q80]

Cellular automata [See also 68Q80]

37B20

递归概念

Notions of recurrence

37B25

Lyapunov函数和稳定性; 吸引子, 排斥子

Lyapunov functions and stability; attractors, repellers

37B30

指标理论, Morse-Conley指标

Index theory, Morse-Conley indices

37B35

类梯度和递归性态; 孤立(局部-极大)不变集

Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets

37B40

拓扑熵

Topological entropy

37B45

动力学中的连续统理论

Continua theory in dynamics

37B50

有限型的多维移位, 贴砖动力学

Multi-dimensional shifts of finite type, tiling dynamics

37B55

非自治动力系统

Nonautonomous dynamical systems

37B99

其它

None of the above, but in this section

37Cxx

光滑动力系统: 一般理论[参见34Cxx, 34Dxx]

Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]

37C05

光滑映射和微分同胚

Smooth mappings and diffeomorphisms

37C10

向量场, , 常微分方程

Vector fields, flows, ordinary differential equations

37C15

拓扑与可微等价性, 共轭, 不变量, , 分类

Topological and differentiable equivalence, conjugacy, invariants, moduli, classification

37C20

一般性质, 结构稳定性

Generic properties, structural stability

37C25

不动点, 周期点, 不动点指数理论

Fixed points, periodic points, fixed-point index theory

37C27

向量场和流的周期轨道

Periodic orbits of vector fields and flows

37C29

同宿和异宿轨道

Homoclinic and heteroclinic orbits

37C30

ζ函数, (Ruelle-Frobenius)迁移算子, 动力系统中其它泛函分析方法

Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems

37C35

轨道增长性

Orbit growth

37C40

光滑遍历理论, 不变测度[参见37Dxx]

Smooth ergodic theory, invariant measures [See also 37Dxx]

37C45

动力系统的维数理论

Dimension theory of dynamical systems

37C50

近似轨道(伪轨道、 影子等)

Approximate trajectories (pseudotrajectories, shadowing, etc.)

37C55

周期和拟周期流与微分同胚

Periodic and quasiperiodic flows and diffeomorphisms

37C60

非自治光滑动力系统[参见37B55]

Nonautonomous smooth dynamical systems [See also 37B55]

37C65

单调流

Monotone flows

37C70

吸引子和排斥子, 拓扑结构

Attractors and repellers, topological structure

37C75

稳定性理论

Stability theory

37C80

对称性等变动力系统

Symmetries, equivariant dynamical systems

37C85

群作用在除ZR叶状结构外的动力学[主要见22Fxx, 也见57R30, 57Sxx]

Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]

37C99

其它

None of the above, but in this section

37Dxx

具有双曲特性的动力系统

Dynamical systems with hyperbolic behavior

37D05

双曲轨道和集合

Hyperbolic orbits and sets

37D10

不变流形理论

Invariant manifold theory

37D15

Morse-Smale系统

Morse-Smale systems

37D20

一致双曲系统(扩张、Anosov、公理A)

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

37D25

非一致双曲系统(Liapunov指数、Pesin理论等)

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)

37D30

部分双曲系统和受控分裂

Partially hyperbolic systems and dominated splittings

37D35

热力学形式体系, 变分原理, 平衡态

Thermodynamic formalism, variational principles, equilibrium states

37D40

几何原点的动力系统和双曲性(测地流和极限圆流等)

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

37D45

奇怪吸引子, 混沌动力学

Strange attractors, chaotic dynamics

37D50

具有奇异性的双曲系统(台球等)

Hyperbolic systems with singularities (billiards, etc.)

37D99

其它

None of the above, but in this section

37Exx

低维动力系统

Low-dimensional dynamical systems

37E05

区间的映射(分段连续, 连续, 光滑)

Maps of the interval (piecewise continuous, continuous, smooth)

37E10

圆的映射

Maps of the circle

37E15

组合动力学(周期轨道型)

Combinatorial dynamics (types of periodic orbits)

37E20

通用性, 重正规化[参见37F25]

Universality, renormalization [See also 37F25]

37E25

树和图的映射

Maps of trees and graphs

37E30

平面和曲面的同胚和微分同胚

Homeomorphisms and diffeomorphisms of planes and surfaces

37E35

曲面上的流

Flows on surfaces

37E40

扭转映射

Twist maps

37E45

旋转数和向量

Rotation numbers and vectors

37E99

其它

None of the above, but in this section

37Fxx

复动力系统[参见30D05, 32H50]

Complex dynamical systems [See also 30D05, 32H50]

37F05

关系和对应

Relations and correspondences

37F10

多项式; 有理映射; 整函数和亚纯函数[参见32A10, 32A20, 32H02, 32H04]

Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]

37F15

扩张映射; 双曲性; 结构稳定性

Expanding maps; hyperbolicity; structural stability

37F20

组合学和拓扑学

Combinatorics and topology

37F25

重正规化

Renormalization

37F30

拟共形方法和Teichmüller理论; 作为动力系统的FuchesKlein

Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems

37F35

共形密度和Hausdorff维数

Conformal densities and Hausdorff dimension

37F40

几何极限

Geometric limits

37F45

动力系统的全纯族; Mandelbrot; 分歧

Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations

37F50

小除子, 旋转域和线性化; FatouJulia

Small divisors, rotation domains and linearization; Fatou and Julia sets

37F75

全纯叶状结构和向量场[参见32M25, 32S65, 34Mxx]

Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]

37F99

其它

None of the above, but in this section

37Gxx

局部和非局部分歧理论[参见34C23, 34K18]

Local and nonlocal bifurcation theory [See also 34C23, 34K18]

37G05

标准型

Normal forms

37G10

奇异点的分歧

Bifurcations of singular points

37G15

极限环和周期轨道的分歧

Bifurcations of limit cycles and periodic orbits

37G20

具有同宿轨道的双曲奇异点

Hyperbolic singular points with homoclinic trajectories

37G25

分歧与非横截相交的关系

Bifurcations connected with nontransversal intersection

37G30

来自分歧的无限非游荡集

Infinite nonwandering sets arising in bifurcations

37G35

吸引子及其分歧

Attractors and their bifurcations

37G40

对称性等变分歧理论

Symmetries, equivariant bifurcation theory

37G99

其它

None of the above, but in this section

37Hxx

随机动力系统[参见15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]]

Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]

37H05

基础, 余圈的一般理论, 代数遍历理论[参见37Axx]

Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]

37H10

生成, 随机差分和微分方程[参见34F05, 34K50, 60H10, 60H15]

Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]

37H15

乘性遍历理论, Lyapunov指数[参见34D08, 37Axx, 37Cxx, 37Dxx]

Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]

37H20

分歧理论[参见37Gxx]

Bifurcation theory [See also 37Gxx]

37H99

其它

None of the above, but in this section

37Jxx

有限维Hamilton, Lagrange, 接触和非完整系统[参见53Dxx, 70Fxx, 70Hxx]

Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]

37J05

一般理论, 与辛几何和拓扑的关系

General theory, relations with symplectic geometry and topology

37J10

辛映射, 不动点

Symplectic mappings, fixed points

37J15

对称性, 不变量, 不变流形, 动量映射, 约化[参见53D20]

Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]

37J20

分歧问题

Bifurcation problems

37J25

稳定性问题

Stability problems

37J30

可积性阻碍(不可积性判据)

Obstructions to integrability (nonintegrability criteria)

37J35

完备可积系统, 相空间的拓扑结构, 积分法

Completely integrable systems, topological structure of phase space, integration methods

37J40

摄动, 标准型, 小除子, KAM理论, Arnol'd扩散

Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion

37J45

周期的, 同宿和异宿轨道; 变分法, -理论方法

Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods

37J50

作用-极小化轨道和测度

Action-minimizing orbits and measures

37J55

接触系统[参见53D10]

Contact systems [See also 53D10]

37J60

非完整动力系统[参见70F25]

Nonholonomic dynamical systems [See also 70F25]

37J99

其它

None of the above, but in this section

37Kxx

无限维Hamilton系统[参见35Axx, 35Qxx]

Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]

37K05

Hamilton结构, 对称性, 变分原理, 守恒律

Hamiltonian structures, symmetries, variational principles, conservation laws

37K10

完备可积系统, 可积性检验, Hamilton结构, 谱系(KdVKPToda)

Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

37K15

逆谱和散射法的完备可积系统的积分法

Integration of completely integrable systems by inverse spectral and scattering methods

37K20

与代数几何、复分析、特殊函数的关系[参见14H70]

Relations with algebraic geometry, complex analysis, special functions [See also 14H70]

37K25

与微分几何的关系

Relations with differential geometry

37K30

与无限维Lie代数及其它代数结构的关系

Relations with infinite-dimensional Lie algebras and other algebraic structures

37K35

Lie-Bäcklund和其它变换

Lie-Bäcklund and other transformations

37K40

孤立子理论, 解的渐近特性

Soliton theory, asymptotic behavior of solutions

37K45

稳定性问题

Stability problems

37K50

分歧问题

Bifurcation problems

37K55

摄动, 无限维系统的KAM

Perturbations, KAM for infinite-dimensional systems

37K60

格动力学[参见37L60]

Lattice dynamics [See also 37L60]

37K65

微分同胚群上和映射与度量流形上的Hamilton系统

Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics

37K99

其它

None of the above, but in this section

37Lxx

无限维耗散动力系统[参见35Bxx, 35Qxx]

Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]

37L05

一般理论, 非线性半群, 发展方程

General theory, nonlinear semigroups, evolution equations

37L10

标准型, 中心流形理论, 分歧理论

Normal forms, center manifold theory, bifurcation theory

37L15

稳定性问题

Stability problems

37L20

对称性

Symmetries

37L25

惯性流形和其它不变吸引集

Inertial manifolds and other invariant attracting sets

37L30

吸引子及其维数, Lyapunov指数

Attractors and their dimensions, Lyapunov exponents

37L40

不变测度

Invariant measures

37L45

双曲性; Lyapunov函数

Hyperbolicity; Lyapunov functions

37L50

非紧半群; 色散方程; Hamilton系统的摄动

Noncompact semigroups; dispersive equations; pertur­bations of Hamiltonian systems

37L55

无限维随机动力系统; 随机方程[参见35R60, 60H10, 60H15]

Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]

37L60

格动力学[参见37K60]

Lattice dynamics [See also 37K60]

37L65

特殊近似法(非线性Galerkin)

Special approximation methods (nonlinear Galerkin, etc.)

37L99

其它

None of the above, but in this section

37Mxx

近似法及动力系统的数值处理[参见65Pxx]

Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]

37M05

仿真

Simulation

37M10

时间序列分析

Time series analysis

37M15

辛积分仪

Symplectic integrators

37M20

分歧问题的计算方法

Computational methods for bifurcation problems

37M25

遍历理论的计算方法(不变测度的逼近, Lyapunov指数的计算, )

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)

37M99

其它

None of the above, but in this section

37Nxx

应用

Applications

37N05

经典和天体力学中的动力系统[主要见70Fxx, 70Hxx, 70Kxx]

Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]

37N10

流体力学、海洋学和气象学中的动力系统[主要见76-XX, 特别地76D05, 76F20, 86A05, 86A10]

Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]

37N15

固体力学中的动力系统[主要见74Hxx]

Dynamical systems in solid mechanics [See mainly 74Hxx]

37N20

物理学其它分支领域(量子力学, 一般相对论, 激光物理)中的动力系统

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)

37N25

生物学中的动力系统[主要见92-XX, 也可见91-XX]

Dynamical systems in biology [See mainly 92-XX, but also 91-XX]

37N30

数值分析中的动力系统

Dynamical systems in numerical analysis

37N35

控制中的动力系统

Dynamical systems in control

37N40

最优化和经济学中的动力系统

Dynamical systems in optimization and economics

37N99

其它

None of the above, but in this section

37Pxx

算术和非Archimedes动力系统[参见11S82, 37A45]

Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45]

37P05

多项式和有理映射

Polynomial and rational maps

37P10

解析和亚纯映射

Analytic and meromorphic maps

37P15

全局基域

Global ground fields

37P20

Archimedes局部基域

Non-Archimedean local ground fields

37P25

有限基域

Finite ground fields

37P30

高度函数; Green函数;不变测度[参见11G50, 14G40]

Height functions; Green functions; invariant measures [See also 11G50, 14G40]

37P35

周期点的算术性质

Arithmetic properties of periodic points

37P40

Archimedes FatouJulia

Non-Archimedean Fatou and Julia sets

37P45

族和模空间

Families and moduli spaces

37P50

Berkovich空间的动力系统

Dynamical systems on Berkovich spaces

37P55

一般代数簇的算术动力学

Arithmetic dynamics on general algebraic varieties

37P99

其它

None of the above, but in this section

39-XX

差分方程与泛函方程

Difference and functional equations

39-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

39-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

39-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

39-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

39-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

39-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

39Axx

差分方程(动力系统, 37-XX; 时间尺度上的动力学方程, 34N05)

Difference equations (For dynamical systems, see 37-XX; for dynamic equations on time scales, see 34N05)

39A05

一般问题

General theory

39A06

线性方程

Linear equations

39A10

差分方程, 加性

Difference equations, additive

39A12

分析课题中的离散式

Discrete version of topics in analysis

39A13

差分方程, 尺度化(q-差分)[参见33Dxx]

Difference equations, scaling (q-differences) [See also 33Dxx]

39A14

偏差分方程

Partial difference equations

39A20

乘法和其它广义差分方程, 例如: Lyness型的

Multiplicative and other generalized difference equations, e.g. of Lyness type

39A21

振荡理论

Oscillation theory

39A22

解的增长性, 有界性及比较

Growth, boundedness, comparison of solutions

39A23

周期解

Periodic solutions

39A24

殆周期解

Almost periodic solutions

39A28

分歧理论

Bifurcation theory

39A30

稳定性理论

Stability theory

39A33

解的复(混沌)性态

Complex (chaotic) behavior of solutions

39A45

复域上的方程

Equations in the complex domain

39A50

随机差分方程

Stochastic difference equations

39A60

应用

Applications

39A70

差分算子[参见47B39]

Difference operators [See also 47B39]

39A99

其它

None of the above, but in this section

39Bxx

泛函方程和不等式[参见30D05]

Functional equations and inequalities [See also 30D05]

39B05

一般问题

General

39B12

迭代理论, 迭代和复合方程[参见26A18, 30D05, 37-XX]

Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]

39B22

实函数方程[参见26A51, 26B25]

Equations for real functions [See also 26A51, 26B25]

39B32

复函数方程[参见30D05]

Equations for complex functions [See also 30D05]

39B42

矩阵与算子方程[参见47Jxx]

Matrix and operator equations [See also 47Jxx]

39B52

更一般域和/或范围上的函数方程

Equations for functions with more general domains and/or ranges

39B55

正交加性和其它条件方程

Orthogonal additivity and other conditional equations

39B62

泛函不等式, 包括次可加性、凸性等[参见26A51, 26B25, 26Dxx]

Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]

39B72

泛函方程和不等式系统

Systems of functional equations and inequalities

39B82

稳定性, 分离, 扩张和相关课题[参见46A22]

Stability, separation, extension, and related topics [See also 46A22]

39B99

其它

None of the above, but in this section

40-XX

序列, 级数, ()和性

Sequences, series, summability

40-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

40-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

40-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

40-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

40-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

40-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

40Axx

无穷极限过程的收敛与发散

Convergence and divergence of infinite limiting processes

40A05

级数与序列的收敛及发散

Convergence and divergence of series and sequences

40A10

积分的收敛与发散

Convergence and divergence of integrals

40A15

连分式的收敛与发散[参见30B70]

Convergence and divergence of continued fractions [See also 30B70]

40A20

无穷乘积的收敛与发散

Convergence and divergence of infinite products

40A25

极限值的逼近(级数求和等)(Euler-Maclaurin求和公式, 65B15)

Approximation to limiting values (summation of series, etc.) (For the Euler-Maclaurin summation formula, see 65B15)

40A30

函数级数与序列的收敛及发散

Convergence and divergence of series and sequences of functions

40A35

理想和统计收敛[参见40G15]

Ideal and statistical convergence [See also 40G15]

40A99

其它

None of the above, but in this section

40Bxx

多重序列与级数

Multiple sequences and series

40B05

多重序列与级数(还应在这节中至少指定一个分类号)

Multiple sequences and series (should also be assigned at least one other classification number in this section)

40B99

其它

None of the above, but in this section

40Cxx

一般可()和性方法

General summability methods

40C05

矩阵法

Matrix methods

40C10

积分法

Integral methods

40C15

函数论方法(包括幂级数法和半连续法)

Function-theoretic methods (including power series methods and semicontinuous methods)

40C99

其它

None of the above, but in this section

40Dxx

()和性的直接定理

Direct theorems on summability

40D05

一般定理

General theorems

40D09

()和性域的结构

Structure of summability fields

40D10

Tauber常数和振荡极限

Tauberian constants and oscillation limits

40D15

收敛因子与可()和性因子

Convergence factors and summability factors

40D20

()和性及方法的有界域

Summability and bounded fields of methods

40D25

包含和等价定理

Inclusion and equivalence theorems

40D99

其它

None of the above, but in this section

40Exx

反演定理

Inversion theorems

40E05

Tauber型定理, 一般理论

Tauberian theorems, general

40E10

增长估计

Growth estimates

40E15

缺项反演定理

Lacunary inversion theorems

40E20

Tauber常数

Tauberian constants

40E99

其它

None of the above, but in this section

40Fxx

绝对和强可()和性(还必须在40-XX中至少指定一个分类号)

Absolute and strong summability (should also be assigned at least one other classification number in Section 40)

40F05

绝对和强可()和性(还必须在40-XX中至少指定一个分类号)

Absolute and strong summability (should also be assigned at least one other classification number in Section 40)

40F99

其它

None of the above, but in this section

40Gxx

()和性的特殊方法

Special methods of summability

40G05

Cesàro, Euler, NörlundHaus­dorff方法

Cesàro, Euler, Nörlund and Hausdorff methods

40G10

Abel, Borel与幂级数方法

Abel, Borel and power series methods

40G15

使用统计收敛的可()和性方法[参见40A35]

Summability methods using statistical convergence [See also 40A35]

40G99

其它

None of the above, but in this section

40Hxx

()和性中的泛函分析法

Functional analytic methods in summability

40H05

()和性中的泛函分析法

Functional analytic methods in summability

40H99

其它

None of the above, but in this section

40Jxx

抽象结构中的可()和性[参见43A55, 46A35, 46B15]

Summability in abstract structures [See also 43A55, 46A35, 46B15]

40J05

抽象结构中的可()和性[参见43A55, 46A35, 46B15](还必须在40-XX中至少指定一个分类号)

Summability in abstract structures [See also 43A55, 46A35, 46B15](should also be assigned at least one other classification number in this section)

40J99

其它

None of the above, but in this section

41-XX

逼近与展开(所有复域中的逼近论, 30E0530E10; 所有三角逼近与插值, 42A1042A15; 数值逼近, 65Dxx)

Approximations and expansions (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx)

41-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

41-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

41-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

41-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

41-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

41-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

41Axx

逼近与展开(所有复域中的逼近论, 30E0530E10; 所有三角逼近与插值, 42A1042A15; 数值逼近, 65Dxx)

Approximations and expansions (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx)

41A05

插值[参见42A1565D05]

Interpolation [See also 42A15 and 65D05]

41A10

多项式逼近(三角多项式逼近, 42A10)

Approximation by polynomials (For approximation by trigonometric polynomials, see 42A10)

41A15

样条逼近

Spline approximation

41A17

逼近不等式(Bernstein, Jackson, Nikol'skiǐ型不等式)

Inequalities in approximation (Bernstein, Jackson, Nikol'skiǐ-type inequalities)

41A20

有理函数逼近

Approximation by rational functions

41A21

Padé逼近

Padé approximation

41A25

收敛速率, 逼近度

Rate of convergence, degree of approximation

41A27

逆定理

Inverse theorems

41A28

同时逼近

Simultaneous approximation

41A29

带约束逼近

Approximation with constraints

41A30

其它特殊函数类的逼近

Approximation by other special function classes

41A35

算子逼近(特别地, 积分算子)

Approximation by operators (in particular, by integral operators)

41A36

正算子逼近

Approximation by positive operators

41A40

饱和

Saturation

41A44

最佳常数

Best constants

41A45

任意线性表达式的逼近

Approximation by arbitrary linear expressions

41A46

任意非线性表达式逼近; 宽度与熵

Approximation by arbitrary nonlinear expressions; widths and entropy

41A50

最佳逼近, Chebyshev系统

Best approximation, Chebyshev systems

41A52

最佳逼近的唯一性

Uniqueness of best approximation

41A55

近似求积分

Approximate quadratures

41A58

级数展开(例如: Taylor, Lids­tone级数, 但非Fourier级数)

Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

41A60

渐近逼近, 渐近展开(最速下降等)[参见30E15]

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]

41A63

多维问题(还应在这节中至少给出一个其它分类号)

Multidimensional problems (should also be assigned at least one other classification number in this section)

41A65

抽象逼近理论(赋范线性空间及其它抽象空间中的逼近)

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

41A80

逼近公式中的余项

Remainders in approximation formulas

41A99

杂题

Miscellaneous topics

42-XX

Euclid空间上的调和分析

Harmonic analysis on Euclidean spaces

42-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

42-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

42-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

42-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

42-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

42-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

42Axx

单变量调和分析

Harmonic analysis in one variable

42A05

三角多项式, 不等式, 极值问题

Trigonometric polynomials, inequalities, extremal problems

42A10

三角逼近

Trigonometric approximation

42A15

三角插值

Trigonometric interpolation

42A16

Fourier系数, 特殊性质函数的Fourier级数, 特殊Fourier级数(自同构理论, 主要见11F30)

Fourier coefficients, Fourier series of functions with special properties, special Fourier series (For automorphic theory, see mainly 11F30)

42A20

Fourier级数与三角级数的收敛性和绝对收敛性

Convergence and absolute convergence of Fourier and trigonometric series

42A24

Fourier级数和三角级数的可求和性和绝对可求和性

Summability and absolute summability of Fourier and trigonometric series

42A32

特殊型三角级数(正系数、单调系数等)

Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

42A38

FourierFourier-Stieltjes变换及其它Fourier型变换

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

42A45

乘子

Multipliers

42A50

共轭函数、共轭级数、奇异积分

Conjugate functions, conjugate series, singular integrals

42A55

三角函数与其它函数的缺项级数; Riesz乘积

Lacunary series of trigonometric and other functions; Riesz products

42A61

概率方法

Probabilistic methods

42A63

三角展开的唯一性, Fourier展开的唯一性, Riemann理论, 局部化

Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization

42A65

函数集的完备性

Completeness of sets of functions

42A70

三角矩问题

Trigonometric moment problems

42A75

经典殆周期函数, 平均周期函数[参见43A60]

Classical almost periodic functions, mean periodic functions [See also 43A60]

42A82

正定函数

Positive definite functions

42A85

卷积, 因子分解

Convolution, factorization

42A99

其它

None of the above, but in this section

42Bxx

多变量调和分析(自同构理论, 主要见11F30)

Harmonic analysis in several variables (For automorphic theory, see mainly 11F30)

42B05

Fourier级数与系数

Fourier series and coefficients

42B08

()和性

Summability

42B10

FourierFourier-Stieltjes变换及其它Fourier型变换

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

42B15

乘子

Multipliers

42B20

奇异积分(Calderón-Zygmund)

Singular integrals (Calderón-Zygmund, etc.)

42B25

极大函数, Littlewood-Paley理论

Maximal functions, Littlewood-Paley theory

42B30

Hp空间

Hp-spaces

42B35

调和分析中的函数空间

Function spaces arising in harmonic analysis

42B37

调和分析与偏微分方程[参见35-XX]

Harmonic analysis and PDE [See also 35-XX]

42B99

其它

None of the above, but in this section

42Cxx

非三角Fourier分析

Nontrigonometric Fourier analysis

42C05

正交函数与多项式, 一般理论[参见33C45, 33C50, 33D45]

Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]

42C10

特殊正交函数的Fourier级数(Legendre多项式、Walsh函数等)

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

42C15

一般调和展开, 框架

General harmonic expansions, frames

42C20

其它调和型变换

Other transformations of harmonic type

42C25

正交级数的唯一性与局部化

Uniqueness and localization for orthogonal series

42C30

函数集的完备性

Completeness of sets of functions

42C40

小波与其它特殊系统

Wavelets and other special systems

42C99

其它

None of the above, but in this section

43-XX

抽象调和分析(拓扑与Lie群的其它分析, 22Exx)

Abstract harmonic analysis (For other analysis on topological and Lie groups, see 22Exx)

43-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

43-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

43-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

43-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

43-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

43-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

43Axx

抽象调和分析(拓扑与Lie群的其它分析, 22Exx)

Abstract harmonic analysis (For other analysis on topological and Lie groups, see 22Exx)

43A05

群与半群等上的测度

Measures on groups and semigroups, etc.

43A07

群、半群等上的平均; 顺从群

Means on groups, semigroups, etc.; amenable groups

43A10

群、半群等上的测度代数

Measure algebras on groups, semigroups, etc.

43A15

群、半群等上的Lp空间与其它函数空间

Lp-spaces and other function spaces on groups, semigroups, etc.

43A17

有序群上的分析, Hp理论

Analysis on ordered groups, Hp-theory

43A20

群、半群等上的L1代数

L1-algebras on groups, semigroups, etc.

43A22

群、半群等上的函数空间的同态与乘子

Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

43A25

局部紧群与其它Abel群上的FourierFourier-Stieltjes变换

Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

43A30

Abel群与半群等上的FourierFourier-Stieltjes变换

Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.

43A32

Fourier型其它变换与算子

Other transforms and operators of Fourier type

43A35

群、半群等上的正定函数

Positive definite functions on groups, semigroups, etc.

43A40

特征标群与对偶对象

Character groups and dual objects

43A45

群、半群等上的谱综合

Spectral synthesis on groups, semigroups, etc.

43A46

特殊集()(薄集、Kronecker集、Helson集、Ditkin集、Sidon集等)

Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

43A50

Fourier级数与逆变换的收敛性

Convergence of Fourier series and of inverse transforms

43A55

群、半群等上的可()和性方法[参见40J05]

Summability methods on groups, semigroups, etc. [See also 40J05]

43A60

群与半群上的殆周期函数及其推广(递归函数、末端函数等); 殆自同构函数

Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions

43A62

超群

Hypergroups

43A65

群、半群等的表示[参见22A10, 22A20, 22Dxx, 22E45]

Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]

43A70

特殊局部紧群与其它Abel群上的分析[参见11R56, 22B05]

Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]

43A75

特殊紧群的分析

Analysis on specific compact groups

43A77

一般紧群的分析

Analysis on general compact groups

43A80

其它特殊Lie群的分析[参见22Exx]

Analysis on other specific Lie groups [See also 22Exx]

43A85

齐性空间上的分析

Analysis on homogeneous spaces

43A90

球面函数[参见22E45, 22E46, 33C55]

Spherical functions [See also 22E45, 22E46, 33C55]

43A95

范畴方法[参见46Mxx]

Categorical methods [See also 46Mxx]

43A99

其它

None of the above, but in this section

44-XX

积分变换, 运算微积分(分数导数与积分, 26A33; Fourier变换, 42A38, 42B10; 分布空间中的积分变换, 46F12; 数值方法, 65R10)

Integral transforms, operational calculus (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10)

44-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

44-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

44-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

44-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

44-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

44-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

44Axx

积分变换, 运算微积分(分数导数与积分, 26A33; Fourier变换, 42A38, 42B10; 分布空间中的积分变换, 46F12; 数值方法, 65R10)

Integral transforms, operational calculus (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10)

44A05

一般变换[参见42A38]

General transforms [See also 42A38]

44A10

Laplace变换

Laplace transform

44A12

Radon变换[参见92C55]

Radon transform [See also 92C55]

44A15

特殊变换(LegendreHilbert)

Special transforms (Legendre, Hilbert, etc.)

44A20

特殊函数的变换

Transforms of special functions

44A30

多重变换

Multiple transforms

44A35

卷积

Convolution

44A40

Mikusiński微积分与其它运算微积分

Calculus of Mikusiński and other operational calculi

44A45

经典运算微积分

Classical operational calculus

44A55

离散运算微积分

Discrete operational calculus

44A60

矩问题

Moment problems

44A99

其它

None of the above, but in this section

45-XX

积分方程

Integral equations

45-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

45-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

45-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

45-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

45-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

45-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

45Axx

线性积分方程

Linear integral equations

45A05

线性积分方程

Linear integral equations

45A99

其它

None of the above, but in this section

45Bxx

Fredholm积分方程

Fredholm integral equations

45B05

Fredholm积分方程

Fredholm integral equations

45B99

其它

None of the above, but in this section

45Cxx

特征值问题[参见34Lxx, 35Pxx, 45P05, 47A75]

Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]

45C05

特征值问题[参见34Lxx, 35Pxx, 45P05, 47A75]

Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]

45C99

其它

None of the above, but in this section

45Dxx

Volterra积分方程[参见34A12]

Volterra integral equations [See also 34A12]

45D05

Volterra积分方程[参见34A12]

Volterra integral equations [See also 34A12]

45D99

其它

None of the above, but in this section

45Exx

奇异积分方程[参见30E20, 30E25, 44A15, 44A35]

Singular integral equations [See also 30E20, 30E25, 44A15, 44A35]

45E05

Cauchy型核的积分方程[参见35J15]

Integral equations with kernels of Cauchy type [See also 35J15]

45E10

卷积型积分方程(Abel, Picard, ToeplitzWiener-Hopf)[参见47B35]

Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]

45E99

其它

None of the above, but in this section

45Fxx

线性积分方程组

Systems of linear integral equations

45F05

非奇异线性积分方程组

Systems of nonsingular linear integral equations

45F10

对偶、三元组等的积分与级数方程

Dual, triple, etc., integral and series equations

45F15

奇异线性积分方程组

Systems of singular linear integral equations

45F99

其它

None of the above, but in this section

45Gxx

非线性积分方程[参见47H30, 47Jxx]

Nonlinear integral equations [See also 47H30, 47Jxx]

45G05

奇异非线性积分方程

Singular nonlinear integral equations

45G10

其它非线性积分方程

Other nonlinear integral equations

45G15

非线性积分方程组

Systems of nonlinear integral equations

45G99

其它

None of the above, but in this section

45Hxx

各种特殊核[参见44A15]

Miscellaneous special kernels [See also 44A15]

45H05

各种特殊核[参见44A15]

Miscellaneous special kernels [See also 44A15]

45H99

其它

None of the above, but in this section

45Jxx

积分-常微分方程[参见34K05, 34K30, 47G20]

Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]

45J05

积分-常微分方程[参见34K05, 34K30, 47G20]

Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]

45J99

其它

None of the above, but in this section

45Kxx

积分-偏微分方程[参见34K30, 35R09, 35R10, 47G20]

Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]

45K05

积分-偏微分方程[参见34K30, 35R09, 35R10, 47G20]

Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]

45K99

其它

None of the above, but in this section

45Lxx

解的理论逼近(数值分析, 65Rxx)

Theoretical approximation of solutions (For numerical analysis, see 65Rxx)

45L05

解的理论逼近(数值分析, 65Rxx)

Theoretical approximation of solutions (For numerical analysis, see 65Rxx)

45L99

其它

None of the above, but in this section

45Mxx

定性特性

Qualitative behavior

45M05

渐近性

Asymptotics

45M10

稳定性理论

Stability theory

45M15

周期解

Periodic solutions

45M20

正解

Positive solutions

45M99

其它

None of the above, but in this section

45Nxx

抽象积分方程, 抽象空间中的积分方程

Abstract integral equations, integral equations in abstract spaces

45N05

抽象积分方程, 抽象空间中的积分方程

Abstract integral equations, integral equations in abstract spaces

45N99

其它

None of the above, but in this section

45Pxx

积分算子[参见47B38, 47G10]

Integral operators [See also 47B38, 47G10]

45P05

积分算子[参见47B38, 47G10]

Integral operators [See also 47B38, 47G10]

45P99

其它

None of the above, but in this section

45Qxx

逆问题

Inverse problems

45Q05

逆问题

Inverse problems

45Q99

其它

None of the above, but in this section

45Rxx

随机积分方程[参见60H20]

Random integral equations [See also 60H20]

45R05

随机积分方程[参见60H20]

Random integral equations [See also 60H20]

45R99

其它

None of the above, but in this section

46-XX

泛函分析(拓扑线性空间上的流形模型, 57Nxx, 58Bxx)

Functional analysis (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx)

46-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

46-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

46-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

46-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

46-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

46-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

46Axx

拓扑线性空间及相关结构(函数空间, 46Exx)

Topological linear spaces and related structures (For function spaces, see 46Exx)

46A03

局部凸空间的一般理论

General theory of locally convex spaces

46A04

局部凸Fréchet空间与(DF)-空间

Locally convex Fréchet spaces and (DF)-spaces

46A08

桶型空间, 有界型空间

Barrelled spaces, bornological spaces

46A11

紧性或可()和性性质确定的空间(核空间、Schwarz空间、Montel空间等)

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

46A13

用归纳或射影极限(LBLF)定义的空间[参见46M40]

Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]

46A16

非局部凸空间(可度量拓扑线性空间、局部有界空间、拟-Banach空间等)

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)

46A17

有界型与相关结构; Mackey收敛等

Bornologies and related structures; Mackey convergence, etc.

46A19

其它“拓扑”线性空间(收敛空间、秩空间、在比R等更一般的有序结构中取值的度量空间等)

Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than R, etc.)

46A20

对偶性理论

Duality theory

46A22

Hahn-Banach型定理; 泛函与算子的扩张及其提升[参见46M10]

Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]

46A25

自反性与半自反性[参见46B10]

Reflexivity and semi-reflexivity [See also 46B10]

46A30

开映射与闭图定理; 完备性(包括B-完备性, Br-完备性)

Open mapping and closed graph theorems; completeness (including B-, Br-completeness)

46A32

线性算子空间; 拓扑张量积; 逼近性质[参见46B28, 46M05, 47L05, 47L20]

Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]

46A35

()和性与基[参见46B15]

Summability and bases [See also 46B15]

46A40

有序拓扑线性空间, 向量格[参见06F20, 46B40, 46B42]

Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]

46A45

序列空间(包括Köthe序列空间)[参见46B45]

Sequence spaces (including Köthe sequence spaces) [See also 46B45]

46A50

拓扑线性空间的紧性; angelic空间等

Compactness in topological linear spaces; angelic spaces, etc.

46A55

拓扑线性空间中的凸集; Choquet理论[参见52A07]

Convex sets in topological linear spaces; Choquet theory [See also 52A07]

46A61

分次Fréchet空间和驯顺算子

Graded Fréchet spaces and tame operators

46A63

拓扑不变量((DN)(Ω))

Topological invariants ((DN), (Ω), etc.)

46A70

Saks空间及其对偶(严格拓扑、混合拓扑、2范数空间、共Saks空间等)

Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)

46A80

模空间

Modular spaces

46A99

其它

None of the above, but in this section

46Bxx

赋范线性空间与Banach空间; Banach(函数空间, 46Exx)

Normed linear spaces and Banach spaces; Banach lattices (For function spaces, see 46Exx)

46B03

Banach空间的同构理论(包括重新赋范)

Isomorphic theory (including renorming) of Banach spaces

46B04

Banach空间的等距理论

Isometric theory of Banach spaces

46B06

Banach空间的渐近理论[参见52A23]

Asymptotic theory of Banach spaces [See also 52A23]

46B07

Banach空间的局部理论

Local theory of Banach spaces

46B08

Banach空间理论中的超积法[参见46M07]

Ultraproduct techniques in Banach space theory [See also 46M07]

46B09

Banach空间理论中的概率方法[参见60Bxx]

Probabilistic methods in Banach space theory [See also 60Bxx]

46B10

对偶性与自反性[参见46A25]

Duality and reflexivity [See also 46A25]

46B15

()和性与基[参见46A35]

Summability and bases [See also 46A35]

46B20

赋范线性空间的几何与结构

Geometry and structure of normed linear spaces

46B22

Radon-Nikodym, Krein-Milman及相关性质[参见46G10]

Radon-Nikodym, Krein-Milman and related properties [See also 46G10]

46B25

一般理论的经典Banach空间

Classical Banach spaces in the general theory

46B26

不可分Banach空间

Nonseparable Banach spaces

46B28

算子空间; 张量积; 逼近性质[参见46A32, 46M05, 47L05, 47L20]

Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]

46B40

有序赋范空间[参见46A40, 46B42]

Ordered normed spaces [See also 46A40, 46B42]

46B42

Banach[参见46A40, 46B40]

Banach lattices [See also 46A40, 46B40]

46B45

Banach序列空间[参见46A45]

Banach sequence spaces [See also 46A45]

46B50

Banach(或赋范)空间中的紧性

Compactness in Banach (or normed) spaces

46B70

赋范线性空间之间的插值()[参见46M35]

Interpolation between normed linear spaces [See also 46M35]

46B80

Banach空间的非线性分类;非线性商

Nonlinear classification of Banach spaces; nonlinear quotients

46B85

离散度量空间嵌入Banach空间;在拓扑和计算机科学中的应用[参见05C12, 68Rxx]

Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx]

46B99

其它

None of the above, but in this section

46Cxx

内积空间及其推广, Hilbert空间(函数空间, 46Exx)

Inner product spaces and their generalizations, Hilbert spaces (For function spaces, see 46Exx)

46C05

Hilbert与准-Hilbert空间: 几何与拓扑(包括半定内积空间)

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

46C07

Hilbert子空间(=算子范围); 互补(Aronszajnde Branges)[参见46B70, 46M35]

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]

46C15

Hilbert空间的特征

Characterizations of Hilbert spaces

46C20

不定内积空间(Krein空间、Pontryagin空间等)[参见47B50]

Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]

46C50

内积的推广(半内积、偏内积等)

Generalizations of inner products (semi-inner products, partial inner products, etc.)

46C99

其它

None of the above, but in this section

46Exx

线性函数空间及其对偶[参见30H05, 32A38, 46F05](函数代数, 46J10)

Linear function spaces and their duals [See also 30H05, 32A38, 46F05] (For function algebras, see 46J10)

46E05

连续、可微或解析函数的格

Lattices of continuous, differentiable or analytic functions

46E10

连续、可微或解析函数的拓扑线性空间

Topological linear spaces of continuous, differentiable or analytic functions

46E15

连续、可微或解析函数的Banach空间

Banach spaces of continuous, differentiable or analytic functions

46E20

连续、可微或解析函数的Hilbert空间

Hilbert spaces of continuous, differentiable or analytic functions

46E22

再生核的Hilbert空间(=[]泛函Hilbert空间)包括de Branges-Rovnyak和其它结构空间)[参见47B32]

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]

46E25

连续、可微或解析函数的环与代数(Banach函数代数, 46J10, 46J15)

Rings and algebras of continuous, differentiable or analytic functions (For Banach function algebras, see 46J10, 46J15)

46E27

测度空间[参见28A33, 46Gxx]

Spaces of measures [See also 28A33, 46Gxx]

46E30

可测函数空间(Lp空间、Orlicz空间、Köthe函数空间、Lorentz空间、重排不变空间、理想空间等)

Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

46E35

Sobolev空间与其它“光滑”函数, 嵌入定理, 迹定理

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

46E39

离散变量函数的Sobolev(和相似类的)空间

Sobolev (and similar kinds of) spaces of functions of discrete variables

46E40

向量值与算子值函数空间

Spaces of vector- and operator-valued functions

46E50

无限维空间上可微或全纯函数空间[参见46G20, 46G25, 47H60]

Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]

46E99

其它

None of the above, but in this section

46Fxx

分布, 广义函数, 分布空间[参见46T30]

Distributions, generalized functions, distribution spaces [See also 46T30]

46F05

测试函数、分布与超分布的拓扑线性空间[参见46E10, 46E35]

Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]

46F10

带分布的运算

Operations with distributions

46F12

分布空间中的积分变换[参见42-XX, 44-XX]

Integral transforms in distribution spaces [See also 42-XX, 44-XX]

46F15

超函数, 解析泛函[参见32A25, 32A45, 32C35, 58J15]

Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]

46F20

解析函数边值的分布与超分布[参见30D40, 30E25, 32A40]

Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]

46F25

无限维空间上的分布[参见58C35]

Distributions on infinite-dimensional spaces [See also 58C35]

46F30

非线性分析的广义函数(Rosin­gerColombeau、非标准等)

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)

46F99

其它

None of the above, but in this section

46Gxx

测度, 积分, 导数, 正则(所有涉及无限维空间)[参见28-XX, 46Txx]

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]

46G05

导数[参见46T20, 58C20, 58C25]

Derivatives [See also 46T20, 58C20, 58C25]

46G10

向量值测度与积分[参见28Bxx, 46B22]

Vector-valued measures and integration [See also 28Bxx, 46B22]

46G12

抽象线性空间上的测度与积分[参见28C20, 46T12]

Measures and integration on abstract linear spaces [See also 28C20, 46T12]

46G15

泛函分析提升理论[参见28A51]

Functional analytic lifting theory [See also 28A51]

46G20

无限维正则[参见32-XX, 46E50, 46T25, 58B12, 58C10]

Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]

46G25

多重线性映射(的空间), 多项式[参见46E50, 46G20, 47H60]

(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]

46G99

其它

None of the above, but in this section

46Hxx

拓扑代数, 赋范环与代数, Banach代数(群代数, 卷积代数与测度代数, 43A10, 43A20)

Topological algebras, normed rings and algebras, Banach algebras (For group algebras, convolution algebras and measure algebras, see 43A10, 43A20)

46H05

拓扑代数的一般理论

General theory of topological algebras

46H10

理想与子代数

Ideals and subalgebras

46H15

拓扑代数的表示

Representations of topological algebras

46H20

拓扑代数的结构, 分类

Structure, classification of topological algebras

46H25

赋范模与Banach, 拓扑模(如果不属于13-XX16-XX)

Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

46H30

拓扑代数中的泛函微积分[参见47A60]

Functional calculus in topological algebras [See also 47A60]

46H35

算子的拓扑代数[主要见47Lxx]

Topological algebras of operators [See mainly 47Lxx]

46H40

自动连续性

Automatic continuity

46H70

非结合拓扑代数[参见46K70, 46L70]

Nonassociative topological algebras [See also 46K70, 46L70]

46H99

其它

None of the above, but in this section

46Jxx

交换Banach代数与交换拓扑代数[参见46E25]

Commutative Banach algebras and commuta­tive topological algebras [See also 46E25]

46J05

交换拓扑代数的一般理论

General theory of commutative topological algebras

46J10

连续函数的Banach代数, 函数代数[参见46E25]

Banach algebras of continuous functions, function algebras [See also 46E25]

46J15

可微函数或解析函数的Banach代数, Hp-空间[参见30H10, 32A35, 32A37, 32A38, 42B30]

Banach algebras of differentiable or analytic functions, Hp-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]

46J20

理想、极大理想、边界

Ideals, maximal ideals, boundaries

46J25

交换拓扑代数的表示

Representations of commutative topological algebras

46J30

子代数

Subalgebras

46J40

交换拓扑代数的结构, 分类

Structure, classification of commutative topological algebras

46J45

Banach代数

Radical Banach algebras

46J99

其它

None of the above, but in this section

46Kxx

具有对合的拓扑(环与)代数[参见16W10]

Topological (rings and) algebras with an involution [See also 16W10]

46K05

具有对合的拓扑代数的一般理论

General theory of topological algebras with involution

46K10

具有对合的拓扑代数的表示

Representations of topological algebras with involution

46K15

Hilbert代数

Hilbert algebras

46K50

具有对合代数的非自伴()代数

Nonselfadjoint (sub)algebras in algebras with involution

46K70

具有对合的非结合拓扑代数[参见46H70, 46L70]

Nonassociative topological algebras with an involution [See also 46H70, 46L70]

46K99

其它

None of the above, but in this section

46Lxx

自伴算子代数(C*-代数、von Neumann(W*-)代数等)[参见22D25, 47Lxx]

Selfadjoint operator algebras (C*-algebras, von Neumann (W*-) algebras, etc.) [See also 22D25, 47Lxx]

46L05

C*-代数的一般理论

General theory of C*-algebras

46L06

C*-代数的张量积

Tensor products of C*-algebras

46L07

算子空间和完备有界映射[参见47L25]

Operator spaces and completely bounded maps [See also 47L25]

46L08

C*-

C*-modules

46L09

C*-代数的自由积

Free products of C*-algebras

46L10

Von Neumann代数的一般理论

General theory of von Neumann algebras

46L30

状态

States

46L35

C*-代数的分类

Classifications of C*-algebras

46L36

因子的分类

Classification of factors

46L37

子因子及其分类

Subfactors and their classification

46L40

自同构

Automorphisms

46L45

C*-代数的分解理论

Decomposition theory for C*-algebras

46L51

非交换测度和积分

Noncommutative measure and integration

46L52

非交换函数空间

Noncommutative function spaces

46L53

非交换概率和统计

Noncommutative probability and statistics

46L54

自由概率和自由算子代数

Free probability and free operator algebras

46L55

非交换动力系统[参见28Dxx, 37Kxx, 37Lxx, 54H20]

Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

46L57

C*-代数的导数、耗散与正半群

Derivations, dissipations and positive semigroups in C*-algebras

46L60

自伴算子代数在物理中的应用[参见46N50, 46N55, 47L90, 81T05, 82B10, 82C10]

Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]

46L65

量化, 形变

Quantizations, deformations

46L70

非结合自伴算子代数[参见46H70, 46K70]

Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]

46L80

K-理论与算子代数(包括循环理论)[参见18F25, 19Kxx, 46M20, 55Rxx, 58J22]

K-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

46L85

非交换拓扑[参见58B32, 58B34, 58J22]

Noncommutative topology [See also 58B32, 58B34, 58J22]

46L87

非交换微分几何[参见58B32, 58B34, 58J22]

Noncommutative differential geometry [See also 58B32, 58B34, 58J22]

46L89

基于C*-代数理论的其它“非交换”数学[参见58B32, 58B34, 58J22]

Other “noncommutative” mathematics based on C*-algebra theory [See also 58B32, 58B34, 58J22]

46L99

其它

None of the above, but in this section

46Mxx

泛函分析中的范畴论方法[参见18-XX]

Methods of category theory in functional analysis [See also 18-XX]

46M05

张量积[参见46A32, 46B28, 47A80]

Tensor products [See also 46A32, 46B28, 47A80]

46M07

超积[参见46B08, 46S20]

Ultraproducts [See also 46B08, 46S20]

46M10

射影与内射对象[参见46A22]

Projective and injective objects [See also 46A22]

46M15

范畴, 函子(K-理论与EXT, 19K33, 46L80, 46M18, 46M20)

Categories, functors (For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20)

46M18

同调方法(正合序列、右逆、提升等)

Homological methods (exact sequences, right inverses, lifting, etc.)

46M20

代数拓扑方法(上同调、层与丛理论等)[参见14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]

Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]

46M35

拓扑向量空间的抽象插值()[参见46B70]

Abstract interpolation of topological vector spaces [See also 46B70]

46M40

归纳与射影极限[参见46A13]

Inductive and projective limits [See also 46A13]

46M99

其它

None of the above, but in this section

46Nxx

泛函分析的各种应用[参见47Nxx]

Miscellaneous applications of functional analysis [See also 47Nxx]

46N10

在最优化、凸分析、数学规划、经济方面的应用

Applications in optimization, convex analysis, mathematical programming, economics

46N20

在微分与积分方程中的应用

Applications to differential and integral equations

46N30

在概率论与统计学中的应用

Applications in probability theory and statistics

46N40

在数值分析中的应用[参见65Jxx]

Applications in numerical analysis [See also 65Jxx]

46N50

在量子物理中的应用

Applications in quantum physics

46N55

在统计物理中的应用

Applications in statistical physics

46N60

在生物学与其它科学中的应用

Applications in biology and other sciences

46N99

其它

None of the above, but in this section

46Sxx

泛函分析的其它(非经典)类型[参见47Sxx]

Other (nonclassical) types of functional analysis [See also 47Sxx]

46S10

域上而非RC或四元数的泛函分析; Archimedes泛函分析[参见12J25, 32P05]

Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]

46S20

非标准泛函分析[参见03H05]

Nonstandard functional analysis [See also 03H05]

46S30

构造性泛函分析[参见03F60]

Constructive functional analysis [See also 03F60]

46S40

模糊泛函分析[参见03E72]

Fuzzy functional analysis [See also 03E72]

46S50

概率度量线性空间中的泛函分析

Functional analysis in probabilistic metric linear spaces

46S60

超空间(超流形)或分次空间上的泛函分析[参见58A50, 58C50]

Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]

46S99

其它

None of the above, but in this section

46Txx

非线性泛函分析[参见47Hxx, 47Jxx, 58Cxx, 58Dxx]

Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]

46T05

无限维流形[参见53Axx, 57N20, 58Bxx, 58Dxx]

Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]

46T10

映射的流形

Manifolds of mappings

46T12

流形上的测度(Gauss、圆柱形的等)和积分(Feynman、路径、Fresnel)[参见28Cxx, 46G12, 60-XX]

Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]

46T20

连续和可微映射[参见46G05]

Continuous and differentiable maps [See also 46G05]

46T25

全纯映射[参见46G20]

Holomorphic maps [See also 46G20]

46T30

非线性空间上的分布和广义函数[参见46Fxx]

Distributions and generalized functions on nonlinear spaces [See also 46Fxx]

46T99

其它

None of the above, but in this section

47-XX

算子理论

Operator theory

47-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

47-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

47-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

47-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

47-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

47-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

47Axx

线性算子的一般理论

General theory of linear operators

47A05

一般理论(伴随的、共轭的、乘积、逆、域、值域等)

General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

47A06

线性关系(多值线性算子)

Linear relations (multivalued linear operators)

47A07

形式(双线性的, 半双线性的, 多线性的)

Forms (bilinear, sesquilinear, multilinear)

47A10

, 预解式

Spectrum, resolvent

47A11

局部谱性质

Local spectral properties

47A12

数值值域, 数值半径

Numerical range, numerical radius

47A13

多变量算子理论(谱、Fredholm)

Several-variable operator theory (spectral, Fredholm, etc.)

47A15

不变子空间[参见47A46]

Invariant subspaces [See also 47A46]

47A16

循环向量, 超循环和混沌算子

Cyclic vector, hypercyclic and chaotic operators

47A20

开拓、扩张、压缩

Dilations, extensions, compressions

47A25

谱集

Spectral sets

47A30

范数(不等式、多范数等)

Norms (inequalities, more than one norm, etc.)

47A35

遍历理论[参见28Dxx, 37Axx]

Ergodic theory [See also 28Dxx, 37Axx]

47A40

散射理论[参见34L25, 35P25, 37K15, 58J50, 81Uxx]

Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]

47A45

收缩算子与非自伴算子的标准模()

Canonical models for contractions and nonselfadjoint operators

47A46

投影或不变子空间的链(), 沿着链的积分等

Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.

47A48

算子综合(=结点)vessels、线性系统、特征函数、实现等

Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.

47A50

未知向量线性算子的方程及不等式

Equations and inequalities involving linear operators, with vector unknowns

47A52

不适定问题, 正则化[参见35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]

Ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]

47A53

()Fredholm算子; 指数理论[参见58B15, 58J20]

(Semi-) Fredholm operators; index theories [See also 58B15, 58J20]

47A55

摄动理论[参见47H14, 58J37, 70H09, 81Q15]

Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

47A56

其值是线性算子的函数(算子与矩阵值函数等, 包括解析和亚纯函数)

Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)

47A57

插值、矩及扩张问题中的算子方法[参见30E05, 42A70, 42A82, 44A60]

Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]

47A58

算子逼近理论

Operator approximation theory

47A60

谓词演算

Functional calculus

47A62

未知算子的线性算子方程

Equations involving linear operators, with operator unknowns

47A63

算子不等式

Operator inequalities

47A64

算子平均、短算子等

Operator means, shorted operators, etc.

47A65

结构理论

Structure theory

47A66

拟三角算子和非拟三角算子, 拟对角算子和非拟对角算子

Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators

47A67

表示理论

Representation theory

47A68

因子分解理论(包括Wiener-Mopf与谱因子分解)

Factorization theory (including Wiener-Hopf and spectral factorizations)

47A70

(广义)特征函数展开; 受控Hilbert空间

(Generalized) eigenfunction expansions; rigged Hilbert spaces

47A75

特征值问题[参见47J10, 49R05]

Eigenvalue problems [See also 47J10, 49R05]

47A80

算子的张量积[参见46M05]

Tensor products of operators [See also 46M05]

47A99

其它

None of the above, but in this section

47Bxx

线性算子的特殊类

Special classes of linear operators

47B06

Riesz算子; 特征值分布; 算子的近似数、算子的s-数、算子的Kolmogorov数、算子的熵数等

Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

47B07

由紧性性质定义的算子

Operators defined by compactness properties

47B10

属于算子理想(核、p-和、Schatten-von Neumann类中等)的算子[参见47L20]

Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]

47B15

Hermite与正规算子(谱测度、谓词演算等)

Hermitian and normal operators (spectral measures, functional calculus, etc.)

47B20

次正规算子、亚正规算子等

Subnormal operators, hyponormal operators, etc.

47B25

对称与自伴算子(无界的)

Symmetric and selfadjoint operators (unbounded)

47B32

再生核Hilbert空间(包括de Brangesde Branges-Rovnyak和其它结构空间 )中算子[参见46E22]

Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]

47B33

复合算子

Composition operators

47B34

核算子

Kernel operators

47B35

Toeplitz算子, Hankel算子, Wiener-Hopf算子[参见45P05, 47G10; 其它积分算子, 参见32A25, 32M15]

Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

47B36

Jacobi(三对角)算子(矩阵)和推广

Jacobi (tridiagonal) operators (matrices) and generalizations

47B37

特殊空间上的算子(加权位移、序列空间上的算子等)

Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

47B38

函数空间上的算子(一般理论)

Operators on function spaces (general)

47B39

差分算子[参见39A70]

Difference operators [See also 39A70]

47B40

谱算子、可分解算子、良有界算子等

Spectral operators, decomposable operators, well-bounded operators, etc.

47B44

增生算子、散逸型算子等

Accretive operators, dissipative operators, etc.

47B47

换位子、求导、初等算子等

Commutators, derivations, elementary operators, etc.

47B48

Banach代数上的算子

Operators on Banach algebras

47B49

变换器, 保持(算子空间上的算子)

Transformers, preservers (operators on spaces of operators)

47B50

不定度量空间上的算子[参见46C50]

Operators on spaces with an indefinite metric [See also 46C50]

47B60

有序空间上的算子

Operators on ordered spaces

47B65

正算子和有序有界算子

Positive operators and order-bounded operators

47B80

随机算子[参见47H40, 60H25]

Random operators [See also 47H40, 60H25]

47B99

其它

None of the above, but in this section

47Cxx

作为代数系统元()的单线性算子

Individual linear operators as elements of algebraic systems

47C05

代数中的算子

Operators in algebras

47C10

*-代数中的算子

Operators in *-algebras

47C15

C*-von Neumann代数中的算子

Operators in C*- or von Neumann algebras

47C99

其它

None of the above, but in this section

47Dxx

线性算子的群和半群, 及其推广和应用

Groups and semigroups of linear operators, their generalizations and applications

47D03

线性算子的群和半群(非线性算子, 47H20; 也见20M20)

Groups and semigroups of linear operators (For nonlinear operators, see 47H20; see also 20M20)

47D06

单参数半群与线性发展方程[参见34G10, 34K30]

One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

47D07

Markov半群及在扩散过程中的应用(Markov过程, 60Jxx)

Markov semigroups and applications to diffusion processes (For Markov processes, see 60Jxx)

47D08

SchrödingerFeynman-Kac半群

Schrödinger and Feynman-Kac semigroups

47D09

算子正弦及余弦函数与高阶Cauchy问题[参见34G10]

Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]

47D60

C-半群, 正则半群

C-semigroups, regularized semigroups

47D62

积分半群

Integrated semigroups

47D99

其它

None of the above, but in this section

47Exx

常微分算子[参见34Bxx, 34Lxx]

Ordinary differential operators [See also 34Bxx, 34Lxx]

47E05

常微分算子[参见34Bxx, 34Lxx](还必须在47-XX中至少指定一个其它分类号)

Ordinary differential operators [See also 34Bxx, 34Lxx](should also be assigned at least one other classification number in section 47)

47E99

其它

None of the above, but in this section

47Fxx

偏微分算子[参见35Pxx, 58Jxx]

Partial differential operators [See also 35Pxx, 58Jxx]

47F05

偏微分算子[参见35Pxx, 58Jxx](还必须在47-XX中至少指定一个其它分类号)

Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)

47F99

其它

None of the above, but in this section

47Gxx

积分算子, 积分-微分算子与伪微分算子[参见58Jxx]

Integral, integro-differential, and pseudodiffe­rential operators [See also 58Jxx]

47G10

积分算子[参见45P05]

Integral operators [See also 45P05]

47G20

积分-微分算子[参见34K30, 35R09, 35R10, 45Jxx, 45Kxx]

Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]

47G30

伪微分算子[参见35Sxx, 58Jxx]

Pseudodifferential operators [See also 35Sxx, 58Jxx]

47G40

位势算子[参见31-XX]

Potential operators [See also 31-XX]

47G99

其它

None of the above, but in this section

47Hxx

非线性算子及其性质(整体及几何方面, 49J53, 58-XX, 特别地, 58Cxx)

Nonlinear operators and their properties (For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx)

47H04

集值算子[参见28B20, 54C60, 58C06]

Set-valued operators [See also 28B20, 54C60, 58C06]

47H05

单调算子和推广

Monotone operators and generalizatios

47H06

增生算子、耗散算子等

Accretive operators, dissipative operators, etc.

47H07

在有序Banach空间或其它有序拓扑向量空间上的单调算子及正算子

Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces

47H08

非紧性测度和凝聚映射、K-集压缩等

Measures of noncompactness and condensing mappings, K-set contractions, etc.

47H09

压缩型映射、非扩张映射、A真映射等

Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

47H10

不动点定理[参见37C25, 54H25, 55M20, 58C30]

Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

47H11

度理论[参见55M25, 58C30]

Degree theory [See also 55M25, 58C30]

47H14

非线性算子的摄动[参见47A55, 58J37, 70H09, 70K60, 81Q51]

Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q51]

47H20

非线性算子半群[参见37L05, 47J35, 54H15, 58D07]

Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

47H25

非线性遍历定理[参见28Dxx, 37Axx, 47A35]

Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35]

47H30

特殊非线性算子(叠加算子、Hammerstein算子、Nemytskiǐ算子、Uryson算子等)[参见45Gxx, 45P05]

Particular nonlinear operators (superposition, Hammer­stein, Nemytskiǐ, Uryson, etc.) [See also 45Gxx, 45P05]

47H40

随机算子[参见47B80, 60H25]

Random operators [See also 47B80, 60H25]

47H60

多线性和多项式算子[参见46G25]

Multilinear and polynomial operators [See also 46G25]

47H99

其它

None of the above, but in this section

47Jxx

涉及非线性算子的方程和不等式[参见46Txx](全局和几何方面, 58-XX)

Equations and inequalities involving nonlinear operators [See also 46Txx] (For global and geometric aspects, see 58-XX)

47J05

涉及非线性算子的方程(一般理论)[参见47H10, 47J25]

Equations involving nonlinear operators (general) [See also 47H10, 47J25]

47J06

非线性不适定问题[参见35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]

Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]

47J07

抽象逆映射和隐函数定理[参见46T20, 58C15]

Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]

47J10

非线性谱理论, 非线性特征值问题[参见49R05]

Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05]

47J15

抽象分歧理论[参见34C23, 37Gxx, 58E07, 58E09]

Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]

47J20

涉及非线性算子的变分和不等式的其它类型(一般理论)[参见49J40]

Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]

47J22

包含变分和其它类型[参见34A60, 49J21, 49K21]

Variational and other types of inclusions [See also 34A60, 49J21, 49K21]

47J25

迭代过程[参见65J15]

Iterative procedures [See also 65J15]

47J30

变分法[参见58Exx]

Variational methods [See also 58Exx]

47J35

非线性发展方程[参见34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]

Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]

47J40

具有滞后算子的方程[参见34C55, 74N30]

Equations with hysteresis operators [See also 34C55, 74N30]

47J99

其它

None of the above, but in this section

47Lxx

算子的线性空间和代数[参见46Lxx]

Linear spaces and algebras of operators [See also 46Lxx]

47L05

算子的线性空间[参见46A3246B28]

Linear spaces of operators [See also 46A32 and 46B28]

47L07

算子的凸集和锥[参见46A55]

Convex sets and cones of operators [See also 46A55]

47L10

Banach空间和其它拓扑线性空间上算子的代数

Algebras of operators on Banach spaces and other topological linear spaces

47L15

具有符号结构的算子代数

Operator algebras with symbol structure

47L20

算子理想[参见47B10]

Operator ideals [See also 47B10]

47L22

多项式理想及多线性映射的理想

Ideals of polynomials and of multilinear mappings

47L25

算子空间(=矩阵赋范空间)[参见46L07]

Operator spaces (= matricially normed spaces) [See also 46L07]

47L30

Hilbert空间上的抽象算子代数

Abstract operator algebras on Hilbert spaces

47L35

套代数, CSL代数

Nest algebras, CSL algebras

47L40

极限代数, C*代数的子代数

Limit algebras, subalgebras of C*-algebras

47L45

对偶代数; 弱闭单生成算子代数

Dual algebras; weakly closed singly generated operator algebras

47L50

算子代数的对偶空间

Dual spaces of operator algebras

47L55

(非自伴)算子代数的表示

Representations of (nonselfadjoint) operator algebras

47L60

无界算子的代数; 算子的偏代数

Algebras of unbounded operators; partial algebras of operators

47L65

叉积代数(解析叉积)

Crossed product algebras (analytic crossed products)

47L70

非结合非自伴算子代数

Nonassociative nonselfadjoint operator algebras

47L75

其它非自伴算子代数

Other nonselfadjoint operator algebras

47L80

特殊型算子(Toeplitz、积分、伪微分等)的代数

Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)

47L90

算子代数应用于物理

Applications of operator algebras to physics

47L99

其它

None of the above, but in this section

47Nxx

算子理论的各种应用[参见46Nxx]

Miscellaneous applications of operator theory [See also 46Nxx]

47N10

在最优化、凸分析、数学规划、经济中的应用

Applications in optimization, convex analysis, mathematical programming, economics

47N20

在微分与积分方程中的应用

Applications to differential and integral equations

47N30

在概率论与统计学中的应用

Applications in probability theory and statistics

47N40

在数值分析中的应用[参见65Jxx]

Applications in numerical analysis [See also 65Jxx]

47N50

在物理科学中的应用

Applications in physics sciences

47N60

在化学和生命科学中的应用

Applications in chemistry and life sciences

47N70

在系统论、回路和控制论中的应用

Applications in systems theory, circuits, and control theory

47N99

其它

None of the above, but in this section

47Sxx

算子理论的其它(非经典)类型[参见46Sxx]

Other (nonclassical) types of operator theory [See also 46Sxx]

47S10

域上而非RC或四元数上的算子理论; Archimedes算子理论

Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory

47S20

非标准算子理论[参见03H05]

Nonstandard operator theory [See also 03H05]

47S30

构造性算子理论[参见03F60]

Constructive operator theory [See also 03F60]

47S40

模糊算子理论[参见03E72]

Fuzzy operator theory [See also 03E72]

47S50

概率度量线性空间中的算子理论[参见54E70]

Operator theory in probabilistic metric linear spaces [See also 54E70]

47S99

其它

None of the above, but in this section

49-XX

变分法与最优控制; 最优化[参见34H05, 34K35, 65Kxx, 90Cxx, 93-XX]

Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]

49-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

49-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

49-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

49-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

49-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

49-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

49Jxx

存在性理论

Existence theories

49J05

一个独立变量的自由问题

Free problems in one independent variable

49J10

两个或更多独立变量的自由问题

Free problems in two or more independent variables

49J15

涉及常微分方程的最优控制问题

Optimal control problems involving ordinary differential equations

49J20

涉及偏微分方程的最优控制问题

Optimal control problems involving partial differential equations

49J21

涉及非微分方程关系的最优控制问题

Optimal control problems involving relations other than differential equations

49J27

抽象空间中的问题[参见90C48, 93C25]

Problems in abstract spaces [See also 90C48, 93C25]

49J30

属于约束类(Lipschitz控制、开关式控制等)的最优解

Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)

49J35

极小极大问题

Minimax problems

49J40

涉及变分不等式的变分法[参见47J20]

Variational methods including variational inequalities [See also 47J20]

49J45

涉及半连续性与收敛性问题的方法; 松弛

Methods involving semicontinuity and convergence; relaxation

49J50

FréchetGateaux可微性[参见46G05, 58C20]

Fréchet and Gateaux differentiability [See also 46G05, 58C20]

49J52

非光滑分析[参见46G05, 58C50]

Nonsmooth analysis [See also 46G05, 58C50]

49J53

集值和变分分析[参见28B20, 47H04, 54C60, 58C06]

Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]

49J55

涉及随机性的问题[参见93E20]

Problems involving randomness [See also 93E20]

49J99

其它

None of the above, but in this section

49Kxx

最优性的条件

optimality conditions

49K05

一个独立变量的自由问题

Free problems in one independent variable

49K10

两个或更多独立变量的自由问题

Free problems in two or more independent variables

49K15

涉及常微分方程的问题

Problems involving ordinary differential equations

49K20

涉及偏微分方程的问题

Problems involving partial differential equations

49K21

涉及非微分方程关系的问题

Problems involving relations other than differential equations

49K27

抽象空间中的问题[参见90C48, 93C25]

Problems in abstract spaces [See also 90C48, 93C25]

49K30

属于约束类的最优解

Optimal solutions belonging to restricted classes

49K35

极小极大问题

Minimax problems

49K40

灵敏度, 稳定性, 适定性[参见90C31]

Sensitivity, stability, well-posedness [See also 90C31]

49K45

涉及随机性的问题[参见93E20]

Problems involving randomness [See also 93E20]

49K99

其它

None of the above, but in this section

49Lxx

Hamilton-Jacobi理论, 包括动态规划

Hamilton-Jacobi theories, including dynamic programming

49L20

动态规划方法

Dynamic programming method

49L25

粘性解

Viscosity solutions

49L99

其它

None of the above, but in this section

49Mxx

数值方法[参见90Cxx, 65Kxx]

Numerical methods [See also 90Cxx, 65Kxx]

49M05

建立在必要条件上的方法

Methods based on necessary conditions

49M15

Newton型方法

Newton-type methods

49M20

松弛型法

Methods of relaxation type

49M25

离散逼近

Discrete approximations

49M27

分解法

Decomposition methods

49M29

涉及对偶性的方法

Methods involving duality

49M30

其它方法

Other methods

49M37

非线性规划型方法[参见90C30, 65Kxx]

Methods of nonlinear programming type [See also 90C30, 65Kxx]

49M99

其它

None of the above, but in this section

49Nxx

杂题

Miscellaneous topics

49N05

线性最优控制问题[参见93C05]

Linear optimal control problems [See also 93C05]

49N10

线性-二次问题

Linear-quadratic problems

49N15

对偶性理论

Duality theory

49N20

周期最优化

Periodic optimization

49N25

脉冲最优控制问题

Impulsive optimal control problems

49N30

不完全信息问题[参见93C41]

Problems with incomplete information [See also 93C41]

49N35

最优反馈综合法[参见93B52]

Optimal feedback synthesis [See also 93B52]

49N45

逆问题

Inverse problems

49N60

解的正则性

Regularity of solutions

49N70

微分对策

Differential games

49N75

追逃对策

Pursuit and evasion games

49N90

最优控制和微分对策的应用[参见90C90, 93C95]

Applications of optimal control and differential games [See also 90C90, 93C95]

49N99

其它

None of the above, but in this section

49Qxx

流形[参见58Exx]

Manifolds [See also 58Exx]

49Q05

极小曲面[参见53A10, 58E12]

Minimal surfaces [See also 53A10, 58E12]

49Q10

形状而非极小曲面的最优化[参见90C90]

Optimization of shapes other than minimal surfaces [See also 90C90]

49Q12

灵敏度分析

Sensitivity analysis

49Q15

几何测度与积分理论, 积分与正规流[参见28A75, 32C30, 58A25, 58C35]

Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]

49Q20

几何测度理论合并中的变分问题

Variational problems in a geometric measure-theoretic setting

49Q99

其它

None of the above, but in this section

49Rxx

算子特征值的变分法[参见47A75]

Variational methods for eigenvalues of opera­tors [See also 47A75]

49R05

算子特征值的变分法[参见47A75](还必须在49-XX中至少指定一个其它分类号)

Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49)

49R99

其它

None of the above, but in this section

49Sxx

物理学的变分原理

Variational principle of physics

49S05

物理学的变分原理(还必须在49-XX中至少指定一个其它分类号)

Variational principle of physics(should also be assigned at least one other classification number in Section 49)

49S99

其它

None of the above, but in this section

51-XX

几何学(代数几何, 14-XX)

Geometry (For algebraic geometry, see 14-XX)

51-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

51-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

51-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

51-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

51-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

51-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

51Axx

线性关联几何

Linear incidence geometry

51A05

一般理论及射影几何

General theory and projective geometries

51A10

同态, 自同构与对偶性

Homomorphism, automorphism and dualities

51A15

平行性结构

Structures with parallelism

51A20

构形定理

Configuration theorems

51A25

代数化[参见12Kxx, 20N05]

Algebraization [See also 12Kxx, 20N05]

51A30

DesarguesPappus几何

Desarguesian and Pappian geometries

51A35

Desargues仿射与射影平面

Non-Desarguesian affine and projective planes

51A40

平移平面与展形

Translation planes and spreads

51A45

可嵌入射影几何的关联结构

Incidence structures imbeddable into projective geometries

51A50

()极几何、辛空间、正交空间

Polar geometry, symplectic spaces, orthogonal spaces

51A99

其它

None of the above, but in this section

51Bxx

非线性关联几何

Nonlinear incidence geometry

51B05

一般理论

General theory

51B10

Möbius几何

Möbius geometries

51B15

Laguerre几何

Laguerre geometries

51B20

Minkowski几何

Minkowski geometries

51B25

Lie几何

Lie geometries

51B99

其它

None of the above, but in this section

51Cxx

环几何(HjelmslevBarbilian)

Ring geometry (Hjelmslev, Barbilian, etc.)

51C05

环几何(HjelmslevBarbilian)

Ring geometry (Hjelmslev, Barbilian, etc.)

51C99

其它

None of the above, but in this section

51Dxx

几何闭包系统

Geometric closure systems

51D05

抽象(Maeda)几何

Abstract (Maeda) geometries

51D10

有交换公理的抽象几何

Abstract geometries with exchange axiom

51D15

有平行性的抽象几何

Abstract geometries with parallelism

51D20

组合几何[参见05B25, 05B35]

Combinatorial geometries [See also 05B25, 05B35]

51D25

子空间的格[参见05B35]

Lattices of subspaces [See also 05B35]

51D30

连续几何与相关论题[参见06Cxx]

Continuous geometries and related topics [See also 06Cxx]

51D99

其它

None of the above, but in this section

51Exx

有限几何与特殊关联结构

Finite geometry and special incidence structures

51E05

一般区组设计[参见05B05]

General block designs [See also 05B05]

51E10

Steiner系统

Steiner systems

51E12

广义四边形, 广义多边形

Generalized quadrangles, generalized polygons

51E14

有限部分几何(一般理论), , 部分展形

Finite partial geometries (general), nets, partial spreads

51E15

仿射与射影平面

Affine and projective planes

51E20

有限射影空间中的组合结构[参见05Bxx]

Combinatorial structures in finite projective spaces [See also 05Bxx]

51E21

块集, 卵形线, k-

Blocking sets, ovals, k-arcs

51E22

Galois空间中的线性码与caps[参见94B05]

Linear codes and caps in Galois spaces [See also 94B05]

51E23

展形与填装问题

Spreads and packing problems

51E24

图的造型与图的几何

Buildings and the geometry of diagrams

51E25

其它有限非线性几何

Other finite nonlinear geometries

51E26

其它有限线性几何

Other finite linear geometries

51E30

其它有限关联结构[参见05B30]

Other finite incidence structures [See also 05B30]

51E99

其它

None of the above, but in this section

51Fxx

度量几何

Metric geometry

51F05

绝对平面

Absolute planes

51F10

绝对空间

Absolute spaces

51F15

反射群, 反射几何[参见20H10, 20H15; Coxeter, 20F55]

Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]

51F20

同余与正交性[参见20H05]

Congruence and orthogonality [See also 20H05]

51F25

正交群与酉群[参见20H05]

Orthogonal and unitary groups [See also 20H05]

51F99

其它

None of the above, but in this section

51Gxx

有序几何(有序关联结构等)

Ordered geometries (ordered incidence structures, etc.)

51G05

有序几何(有序关联结构等)

Ordered geometries (ordered incidence structures, etc.)

51G99

其它

None of the above, but in this section

51Hxx

拓扑几何

Topological geometry

51H05

一般理论

General theory

51H10

拓扑线性关联结构

Topological linear incidence structures

51H15

拓扑非线性关联结构

Topological nonlinear incidence structures

51H20

流形上的拓扑几何[参见57-XX]

Topological geometries on manifolds [See also 57-XX]

51H25

具有可微结构的几何[参见53Cxx, 53C70]

Geometries with differentiable structure [See also 53Cxx, 53C70]

51H30

具有代数流形结构的几何[参见14-XX]

Geometries with algebraic manifold structure [See also 14-XX]

51H99

其它

None of the above, but in this section

51Jxx

关联群

Incidence groups

51J05

一般理论

General theory

51J10

射影关联群

Projective incidence groups

51J15

运动空间

Kinematic spaces

51J20

拟域与拟代数表示[参见12K05, 16Y30]

Representation by near-fields and near-algebras [See also 12K05, 16Y30]

51J99

其它

None of the above, but in this section

51Kxx

距离几何

Distance geometry

51K05

一般理论

General theory

51K10

综合微分几何

Synthetic differential geometry

51K99

其它

None of the above, but in this section

51Lxx

几何有序结构[参见53C75]

Geometric order structures [See also 53C75]

51L05

不可微曲线的序几何

Geometry of orders of nondifferentiable curves

51L10

直接可微曲线

Directly differentiable curves

51L15

通过直接法的n极点定理

n-vertex theorems via direct methods

51L20

曲面的序几何

Geometry of orders of surfaces

51L99

其它

None of the above, but in this section

51Mxx

实几何与复几何

Real and complex geometry

51M04

Euclid几何中的基本问题

Elementary problems in Euclidean geometries

51M05

Euclid几何(一般问题)及其推广

Euclidean geometries (general) and generalizations

51M09

双曲几何与椭圆几何中的基本问题

Elementary problems in hyperbolic and elliptic geometries

51M10

双曲几何与椭圆几何(一般问题)及其推广

Hyperbolic and elliptic geometries (general) and generalizations

51M15

几何构造

Geometric constructions

51M16

不等式与极值问题(凸问题, 52A40)

Inequalities and extremum problems (For convex problems, see 52A40)

51M20

多面体与多胞形; 正则图, 空间除法[参见51F15]

Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]

51M25

长度、面积与体积[参见26B15]

Length, area and volume [See also 26B15]

51M30

线几何及其推广[参见53A25]

Line geometries and their generalizations [See also 53A25]

51M35

射影几何中基本流形的综合处理(Grassmannians, Veronesians及其推广)[参见14M15]

Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]

51M99

其它

None of the above, but in this section

51Nxx

解析几何与画法几何

Analytic and descriptive geometry

51N05

画法几何[参见65D17, 68U07]

Descriptive geometry [See also 65D17, 68U07]

51N10

仿射解析几何

Affine analytic geometry

51N15

射影解析几何

Projective analytic geometry

51N20

Euclid解析几何

Euclidean analytic geometry

51N25

具有其它变换群的解析几何

Analytic geometry with other transformation groups

51N30

经典群几何[参见20Gxx, 14L35]

Geometry of classical groups [See also 20Gxx, 14L35]

51N35

经典代数几何问题[参见14Nxx]

Questions of classical algebraic geometry [See also 14Nxx]

51N99

其它

None of the above, but in this section

51Pxx

几何与物理学(还应在70-XX86-XX部分至少指定一个分类号)

Geometry and physics (should also be assigned at least one other classification number from Sections 70-86)

51P05

几何与物理学(还应在70-XX86-XX部分至少指定一个分类号)

Geometry and physics (should also be assigned at least one other classification number from Sections 70-86)

51P99

其它

None of the above, but in this section

52-XX

凸几何与离散几何

Convex and discrete geometry

52-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

52-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

52-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

52-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

52-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

52-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

52Axx

一般凸性

General convexity

52A01

公理化与广义凸性

Axiomatic and generalized convexity

52A05

没有维数约束的凸集

Convex sets without dimension restrictions

52A07

拓扑向量空间中的凸集[参见46A55]

Convex sets in topological vector spaces [See also 46A55]

52A10

2维凸集(包括凸曲线)[参见53A04]

Convex sets in 2 dimensions (including convex curves) [See also 53A04]

52A15

3维凸集(包括凸曲面)[参见53A05, 53C45]

Convex sets in 3 dimensions (including convex surfaces) [See also 53A05, 53C45]

52A20

n维凸集(包括凸超曲面)[参见53A07, 53C45]

Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]

52A21

有限维Banach空间(包括特殊范数、高维环面等)[参见46Bxx]

Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]

52A22

随机凸集与积分几何[参见53C65, 60D05]

Random convex sets and integral geometry [See also 53C65, 60D05]

52A23

凸体渐近论[参见46B06]

Asymptotic theory of convex bodies [See also 46B06]

52A27

用凸集逼近

Approximation by convex sets

52A30

凸集的变量(星形的、(m, n)-凸等)

Variants of convex sets (star-shaped, (m, n)-convex, etc.)

52A35

Helly型定理与几何横截理论

Helly-type theorems and geometric transversal theory

52A37

组合凸性的其它问题

Other problems of combinatorial convexity

52A38

长度、面积、体积[参见26B15, 28A75, 49Q20]

Length, area, volume [See also 26B15, 28A75, 49Q20]

52A39

混合体积及相关论题

Mixed volumes and related topics

52A40

不等式与极值问题

Inequalities and extremum problems

52A41

凸函数与凸规划[参见26B25, 90C25]

Convex functions and convex programs [See also 26B25, 90C25]

52A55

球面与双曲凸性

Spherical and hyperbolic convexity

52A99

其它

None of the above, but in this section

52Bxx

多胞形与多面体

Polytopes and polyhedra

52B05

组合性质(面数、最短路径等)[参见05Cxx]

Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]

52B10

三维多胞形

Three-dimensional polytopes

52B11

n-维多胞形

n-dimensional polytopes

52B12

特殊多胞形(线性规划、中心对称等)

Special polytopes (linear programming, centrally symmetric, etc.)

52B15

多胞形的对称性质

Symmetry properties of polytopes

52B20

格多胞形(包括与交换代数及代数几何的关系)[参见06A11, 13F20, 13Hxx]

Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

52B22

Shellability

Shellability

52B35

Gale与其它图()

Gale and other diagrams

52B40

拟阵(在凸多胞形前后关系中的实现、组合结构中的凸性等)[参见05B35, 52Cxx]

Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]

52B45

剖分与赋值(Hilbert第三问题等)

Dissections and valuations (Hilbert’s third problem, etc.)

52B55

关于凸性的计算方面(计算几何与算法, 68Q25, 68U05; 数值算法, 65Yxx)[参见68Uxx]

Computational aspects related to convexity (For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx) [See also 68Uxx]

52B60

多胞形的等周问题

Isoperimetric problems for polytopes

52B70

多面体流形

Polyhedral manifolds

52B99

其它

None of the above, but in this section

52Cxx

离散几何

Discrete geometry

52C05

格与2维凸体[参见11H06, 11H31, 11P21]

Lattices and convex bodies in 2 dimensions [See also 11H06, 11H31, 11P21]

52C07

格与n维凸体[参见11H06, 11H31, 11P21]

Lattices and convex bodies in n dimensions [See also 11H06, 11H31, 11P21]

52C10

Erdös问题与离散几何的相关论题[参见11Hxx]

Erdös problems and related topics of discrete geometry [See also 11Hxx]

52C15

填装与2维覆盖[参见05B40, 11H31]

Packing and covering in 2 dimensions [See also 05B40, 11H31]

52C17

填装与n维覆盖[参见05B40, 11H31]

Packing and covering in n dimensions [See also 05B40, 11H31]

52C20

2维贴砖[参见05B45, 51M20]

Tilings in 2 dimensions [See also 05B45, 51M20]

52C22

n维贴砖[参见05B45, 51M20]

Tilings in n dimensions [See also 05B45, 51M20]

52C23

拟晶体、非周期贴砖

Quasicrystals, aperiodic tilings

52C25

结构的刚性及挠性[参见70B15]

Rigidity and flexibility of structures [See also 70B15]

52C26

圆填装和离散共形几何

Circle packings and discrete conformal geometry

52C30

线()和伪线(伪边)的平面排列

Planar arrangements of lines and pseudolines

52C35

, 平坦, 超平面的排列[参见32S22]

Arrangements of points, flats, hyperplanes [See also 32S22]

52C40

定向拟阵

Oriented matroids

52C45

几何结构的组合复杂性[参见68U05]

Combinatorial complexity of geometric structures [See also 68U05]

52C99

其它

None of the above, but in this section

53-XX

微分几何(微分拓扑, 57Rxx; 可微流形的基础问题, 58Axx)

Differential geometry (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)

53-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

53-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

53-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

53-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

53-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

53-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

53Axx

经典微分几何

Classical differential geometry

53A04

Euclid空间中的曲线

Curves in Euclidean space

53A05

Euclid空间中的曲面

Surfaces in Euclidean space

53A07

Euclid n维空间中的高维及高余维曲面

Higher-dimensional and -codimensional surfaces in Euclidean n-space

53A10

极小曲面、具有指定平均曲率的曲面[参见49Q05, 49Q10, 53C42]

Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

53A15

仿射微分几何

Affine differential geometry

53A17

运动学

Kinematics

53A20

射影微分几何

Projective differential geometry

53A25

微分线几何

Differential line geometry

53A30

共形微分几何

Conformal differential geometry

53A35

Euclid微分几何

Non-Euclidean differential geometry

53A40

其它特殊微分几何

Other special differential geometries

53A45

向量与张量分析

Vector and tensor analysis

53A55

微分不变量(局部理论), 几何对象

Differential invariants (local theory), geometric objects

53A60

罗几何[参见14C21, 20N05]

Geometry of webs [See also 14C21, 20N05]

53A99

其它

None of the above, but in this section

53Bxx

局部微分几何

Local differential geometry

53B05

线性和仿射联络

Linear and affine connections

53B10

射影联络

Projective connections

53B15

其它联络

Other connections

53B20

局部Riemann几何

Local Riemannian geometry

53B21

Riemann几何方法

Methods of Riemannian geometry

53B25

局部子流形[参见53C40]

Local submanifolds [See also 53C40]

53B30

Lorentz度量, 不定度量

Lorentz metrics, indefinite metrics

53B35

HermiteKähler结构[参见32Cxx]

Hermitian and Kählerian structures [See also 32Cxx]

53B40

Finsler空间和推广(面积度量)

Finsler spaces and generalizations (areal metrics)

53B50

在物理上的应用

Applications to physics

53B99

其它

None of the above, but in this section

53Cxx

整体微分几何[参见51H25, 58-XX](相关丛理论, 55Rxx, 57Rxx)

Global differential geometry [See also 51H25, 58-XX] (For related bundle theory, see 55Rxx, 57Rxx)

53C05

联络, 一般理论

Connections, general theory

53C07

向量丛(Hermite-Einstein-Yang-Mills)上的特殊联络和度量[参见32Q20]

Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]

53C08

Gerbes, 微分特征标: 微分几何方面

Gerbes, differential characters: differential geometric aspects

53C10

G-结构

G-structures

53C12

叶状结构物(微分几何方面)[参见57R30, 57R32]

Foliations (differential geometric aspects) [See also 57R30, 57R32]

53C15

流形上的一般几何结构(殆复结构、殆积结构等)

General geometric structures on manifolds (almost complex, almost product structures, etc.)

53C17

Riemann几何

Sub-Riemannian geometry

53C20

整体Riemann几何, 包括扭[参见31C12, 58B20]

Global Riemannian geometry, including pinching [See also 31C12, 58B20]

53C21

Riemann几何方法, 包括偏微分方程方法; 曲率限制[参见58J60]

Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

53C22

测地线[参见58E10]

Geodesics [See also 58E10]

53C23

整体几何和拓扑方法(属于Gromov); 度量空间上的微分几何分析

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

53C24

刚性结果

Rigidity results

53C25

特殊Riemann流形(EinsteinSasaki)

Special Riemannian manifolds (Einstein, Sasakian, etc.)

53C26

Kähler和四元数Kähler几何, “特殊”几何

Hyper-Kähler and quaternionic Kähler geometry, “special” geometry

53C27

自旋和自旋c几何

Spin and Spinc geometry

53C28

扭子方法[参见32L25]

Twistor methods [See also 32L25]

53C29

完整的问题

Issues of holonomy

53C30

齐次流形[参见14M15, 14M17, 32M10, 57T15]

Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

53C35

对称空间[参见32M15, 57T15]

Symmetric spaces [See also 32M15, 57T15]

53C38

校准和校准几何

Calibrations and calibrated geometries

53C40

整体子流形[参见53B25]

Global submanifolds [See also 53B25]

53C42

浸入(极小曲率、规定曲率、紧密的等)[参见49Q05, 49Q10, 53A10, 57R40, 57R42]

Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

53C43

调和映射的微分几何方面[参见58E20]

Differential geometric aspects of harmonic maps [See also 58E20]

53C44

几何发展方程(平均曲率流、Ricci流等)

Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

53C45

整体曲面论(凸曲面属于A.D.Aleksandrov)

Global surface theory (convex surfaces à la A. D. Aleksandrov)

53C50

Lorentz流形, 不定度量流形

Lorentz manifolds, manifolds with indefinite metrics

53C55

HermiteKähler流形[参见32Cxx]

Hermitian and Kählerian manifolds [See also 32Cxx]

53C56

其它复微分几何[参见32Cxx]

Other complex differential geometry [See also 32Cxx]

53C60

Finsler空间和推广(面积度量)[参见58B20]

Finsler spaces and generalizations (areal metrics) [See also 58B20]

53C65

积分几何[参见52A22, 60D05]; 微分形式、流等[主要见58Axx]

Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

53C70

直接法(Busemann G-空间等)

Direct methods (G-spaces of Busemann, etc.)

53C75

几何序, 序几何[参见51Lxx]

Geometric orders, order geometry [See also 51Lxx]

53C80

应用于物理

Applications to physics

53C99

其它

None of the above, but in this section

53Dxx

辛几何, 接触几何[参见37Jxx, 70Gxx, 70Hxx]

Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]

53D05

辛流形, 一般理论

Symplectic manifolds, general

53D10

接触流形, 一般理论

Contact manifolds, general

53D12

Lagrange子流形; Maslov指数

Lagrangian submanifolds; Maslov index

53D15

殆接触和殆辛流形

Almost contact and almost symplectic manifolds

53D17

Poisson流形; Poisson广群和代数体

Poisson manifolds; Poisson groupoids and algebroids

53D18

广义几何(属于Hitchin)

Generalized geometries (à la Hitchin)

53D20

动量映射; 辛约化

Momentum maps; symplectic reduction

53D22

典型变换

Canonical transformations

53D25

测地流

Geodesic flows

53D30

模空间的辛结构

Symplectic structures of moduli spaces

53D35

辛的整体理论和接触流形[参见57Rxx]

Global theory of symplectic and contact manifolds [See also 57Rxx]

53D37

镜像对称, 辛方面; 同调镜像对称; Fukaya范畴[参见14J33]

Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]

53D40

Floer()同调和上同调, 辛方面

Floer homology and cohomology, symplectic aspects

53D42

辛域论; 接触同调

Symplectic field theory; contact homology

53D45

Gromov-Witten不变量, 量子上同调, Frobenius流形[参见14N35]

Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

53D50

几何量子化

Geometric quantization

53D55

变形量子化, 星积

Deformation quantization, star products

53D99

其它

None of the above, but in this section

53Zxx

应用于物理

Applications to physics

53Z05

应用于物理

Applications to physics

53Z99

其它

None of the above, but in this section

54-XX

一般拓扑学(所有维流形的拓扑, 57Nxx)

General topology (For the topology of manifolds of all dimensions, see 57Nxx)

54-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

54-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

54-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

54-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

54-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

54-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

54Axx

一般理论

Generalities

54A05

拓扑空间和推广(闭包空间等)

Topological spaces and generalizations (closure spaces, etc.)

54A10

单集上的多拓扑(拓扑变化, 拓扑比较, 拓扑格)

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

54A15

综合拓扑结构

Syntopogeneous structures

54A20

一般拓扑学的收敛性(序列、滤子、极限、收敛空间等)

Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

54A25

基数性质(基数函数和不等式, 离散子集)[参见03Exx](超滤子, 54D80)

Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] (For ultrafilters, see 54D80)

54A35

相容性和独立结果[参见03E35]

Consistency and independence results [See also 03E35]

54A40

模糊拓扑[参见03E72]

Fuzzy topology [See also 03E72]

54A99

其它

None of the above, but in this section

54Bxx

基本构造

Basic constructions

54B05

子空间

Subspaces

54B10

积空间

Product spaces

54B15

商空间, 分解

Quotient spaces, decompositions

54B17

附加空间和相似构造

Adjunction spaces and similar constructions

54B20

超空间

Hyperspaces

54B30

范畴方法[参见18B30]

Categorical methods [See also 18B30]

54B35

Spectra

54B40

预层和层[参见18F20]

Presheaves and sheaves [See also 18F20]

54B99

其它

None of the above, but in this section

54Cxx

映射和由映射定义的一般类型空间

Maps and general types of spaces defined by maps

54C05

连续映射

Continuous maps

54C08

弱连续性和广义连续性

Weak and generalized continuity

54C10

拓扑空间的特殊映射(开、闭、完美等)

Special maps on topological spaces (open, closed, perfect, etc.)

54C15

(保核)收缩

Retraction

54C20

映射的扩张

Extension of maps

54C25

嵌入

Embedding

54C30

实值函数[参见26-XX]

Real-valued functions [See also 26-XX]

54C35

函数空间[参见46Exx, 58D15]

Function spaces [See also 46Exx, 58D15]

54C40

函数空间的代数性质[参见46J10]

Algebraic properties of function spaces [See also 46J10]

54C45

C-C*-嵌入

C- and C*-embedding

54C50

由函数定义的特殊集[参见26A21]

Special sets defined by functions [See also 26A21]

54C55

绝对邻域开拓子, 绝对开拓子, 绝对邻域收缩核(ANR), 绝对收缩核空间(一般性质)[参见55M15]

Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]

54C56

形状理论[参见55P55, 57N25]

Shape theory [See also 55P55, 57N25]

54C60

集值映射[参见26E25, 28B20, 47H04, 58C06]

Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]

54C65

选择[参见28B20]

Selections [See also 28B20]

54C70

Entropy

54C99

其它

None of the above, but in this section

54Dxx

一般性质

Fairly general properties

54D05

连通和局部连通空间(一般方面)

Connected and locally connected spaces (general aspects)

54D10

下分离公理(T0-T3)

Lower separation axioms (T0-T3, etc.)

54D15

高分离公理(完全正则的、正规的、完备或集体式正规的等)

Higher separation axioms (completely regular, normal, perfectly or collection-wise normal, etc.)

54D20

非紧覆盖性质(仿紧性、Lindelöf)

Noncompact covering properties (paracompact, Lindelöf, etc.)

54D25

P-极小”和“P-闭”空间

P-minimal” and “P-closed” spaces

54D30

紧性

Compactness

54D35

空间的扩张(紧化、超紧化、完备化等)

Extensions of spaces (compactifications, supercom­pactifications, completions, etc.)

54D40

剩余

Remainders

54D45

局部紧性, σ-紧性

Local compactness, σ-compactness

54D50

K-空间

K-spaces

54D55

序列空间

Sequential spaces

54D60

实紧性和实紧化

Realcompactness and realcompactification

54D65

可分性

Separability

54D70

基性质

Base properties

54D80

空间的特殊构造(超滤子空间等)

Special constructions of spaces (spaces of ultrafilters, etc.)

54D99

其它

None of the above, but in this section

54Exx

有较丰富结构的空间

Spaces with richer structures

54E05

邻近结构和推广

Proximity structures and generalizations

54E15

一致结构和推广

Uniform structures and generalizations

54E17

近性空间

Nearness spaces

54E18

p-空间、M-空间、σ-空间等

p-spaces, M-spaces, σ-spaces, etc.

54E20

可层化空间、宇宙空间等

Stratifiable spaces, cosmic spaces, etc.

54E25

半度量空间

Semimetric spaces

54E30

Moore空间

Moore spaces

54E35

度量空间, 可度量性

Metric spaces, metrizability

54E40

度量空间上的特殊映射

Special maps on metric spaces

54E45

(局部紧)度量空间

Compact (locally compact) metric spaces

54E50

完备度量空间

Complete metric spaces

54E52

Baire范畴, Baire空间

Baire category, Baire spaces

54E55

双拓扑

Bitopologies

54E70

概率度量空间

Probabilistic metric spaces

54E99

其它

None of the above, but in this section

54Fxx

特殊性质

Special properties

54F05

线性有序拓扑空间, 广义有序空间, 偏序空间[参见06B30, 06F30]

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]

54F15

延拓和推广

Continua and generalizations

54F35

高维局部连通性[参见55Mxx, 55Nxx]

Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]

54F45

维数论[参见55M10]

Dimension theory [See also 55M10]

54F50

维数≤1的空间; 曲线, 无圈曲线[参见26A03]

Spaces of dimension ≤1; curves, dendrites [See also 26A03]

54F55

单凝聚, 多凝聚

Unicoherence, multicoherence

54F65

特殊空间的拓扑特征

Topological characterizations of particular spaces

54F99

其它

None of the above, but in this section

54Gxx

独特空间

Peculiar spaces

54G05

极不连通空间、F-空间等

Extremally disconnected spaces, F-spaces, etc.

54G10

P-空间

P-spaces

54G12

散射空间

Scattered spaces

54G15

病态空间

Pathological spaces

54G20

反例

Counterexamples

54G99

其它

None of the above, but in this section

54Hxx

与其它结构的联系, 应用

Connections with other structures, applications

54H05

描述集合论(Borel、解析、投射等集的拓扑方面)[参见03E15, 26A21, 28A05]

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]

54H10

代数系的拓扑表示[参见22-XX]

Topological representations of algebraic systems [See also 22-XX]

54H11

拓扑群[参见22A05]

Topological groups [See also 22A05]

54H12

拓扑格等[参见06B30, 06F30]

Topological lattices, etc. [See also 06B30, 06F30]

54H13

拓扑域、拓扑环等[参见12Jxx](代数方面, 13Jxx, 16W80)

Topological fields, rings, etc. [See also 12Jxx] (For algebraic aspects, see 13Jxx, 16W80)

54H15

变换群和半群[参见20M20, 22-XX, 57Sxx]

Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]

54H20

拓扑动力学[参见28Dxx, 37Bxx]

Topological dynamics [See also 28Dxx, 37Bxx]

54H25

不动点定理和叠合定理[参见47H10, 55M20]

Fixed-point and coincidence theorems [See also 47H10, 55M20]

54H99

其它

None of the above, but in this section

54Jxx

非标准拓扑[参见03H05]

Nonstandard topology [See also 03H05]

54J05

非标准拓扑[参见03H05]

Nonstandard topology [See also 03H05]

54J99

其它

None of the above, but in this section

55-XX

代数拓扑学

Algebraic topology

55-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

55-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

55-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

55-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

55-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

55-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

55Mxx

经典课题(Euclid空间的拓扑学和流形, 57Nxx)

Classical topics (For the topology of Euclidean spaces and manifolds, see 57Nxx)

55M05

对偶性

Duality

55M10

维数论[参见54F45]

Dimension theory [See also 54F45]

55M15

绝对邻域收缩核[参见54C55]

Absolute neighborhood retracts [See also 54C55]

55M20

不动点和叠合[参见54H25]

Fixed points and coincidences [See also 54H25]

55M25

, 分枝数

Degree, winding number

55M30

空间的Ljusternik-Schnirelman (Lyusternik-Shnirelman)范畴

Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space

55M35

有限变换群(包括Smith理论)[参见57S17]

Finite groups of transformations (including Smith theory) [See also 57S17]

55M99

其它

None of the above, but in this section

55Nxx

同调和上同调理论[参见57Txx]

Homology and cohomology theories [See also 57Txx]

55N05

Čech

Čech types

55N07

Steenrod-Sitnikov同调

Steenrod-Sitnikov homologies

55N10

奇异理论

Singular theory

55N15

K-理论[参见19Lxx](代数K-理论, 18F25, 19-XX)

K-theory [See also 19Lxx] (For algebraic K-theory, see 18F25, 19-XX)

55N20

广义(非常)同调和上同调理论

Generalized (extraordinary) homology and cohomology theories

55N22

加边和配边理论, 形式群定律[参见14L05, 19L41, 57R75, 57R77, 57R85, 57R90]

Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]

55N25

有局部系数的同调, 等变化上同调

Homology with local coefficients, equivariant cohomology

55N30

层上同调[参见18F20, 32C35, 32L10]

Sheaf cohomology [See also 18F20, 32C35, 32L10]

55N32

轨形上同调

Orbifold cohomology

55N33

相交同调和上同调

Intersection homology and cohomology

55N34

椭圆上同调

Elliptic cohomology

55N35

其它同调理论

Other homology theories

55N40

同调论公理和唯一性定理

Axioms for homology theory and uniqueness theorems

55N45

积和交

Products and intersections

55N91

等变化同调和上同调[参见19L47]

Equivariant homology and cohomology [See also 19L47]

55N99

其它

None of the above, but in this section

55Pxx

同伦理论(简单同伦型, 57Q10)

Homotopy theory (For simple homotopy type, see 57Q10)

55P05

同伦扩张性质, 上纤维化

Homotopy extension properties, cofibrations

55P10

同伦等价

Homotopy equivalences

55P15

同伦型的分类

Classification of homotopy type

55P20

Eilenberg-Mac Lane空间

Eilenberg-Mac Lane spaces

55P25

Spanier-Whitehead对偶性

Spanier-Whitehead duality

55P30

Eckmann-Hilton对偶性

Eckmann-Hilton duality

55P35

圈空间

Loop spaces

55P40

同纬映射

Suspensions

55P42

稳定同伦理论,

Stable homotopy theory, spectra

55P43

具有附加结构的谱(EA、环谱等)

Spectra with additional structure (E, A, ring spectra, etc.)

55P45

H-空间和对偶

H-spaces and duals

55P47

无限圈空间

Infinite loop spaces

55P48

圈空间机器, operads[参见18D50]

Loop space machines, operads [See also 18D50]

55P50

String拓扑

String topology

55P55

形状理论[参见54C56, 55Q07]

Shape theory [See also 54C56, 55Q07]

55P57

真同伦理论

Proper homotopy theory

55P60

局部化和完备化

Localization and completion

55P62

有理同伦理论

Rational homotopy theory

55P65

同伦函子

Homotopy functors

55P91

等变化同伦理论[参见19L47]

Equivariant homotopy theory [See also 19L47]

55P92

等变同伦论与非等变同伦论之间的关系

Relations between equivariant and nonequivariant homotopy theory

55P99

其它

None of the above, but in this section

55Qxx

同伦群

Homotopy groups

55Q05

同伦群, 一般理论; 同伦类集合

Homotopy groups, general; sets of homotopy classes

55Q07

形状群

Shape groups

55Q10

稳定同伦群

Stable homotopy groups

55Q15

Whitehead积和推广

Whitehead products and generalizations

55Q20

, 联和单空间同伦群

Homotopy groups of wedges, joins, and simple spaces

55Q25

Hopf不变量

Hopf invariants

55Q35

同伦群运算

Operations in homotopy groups

55Q40

球同伦群

Homotopy groups of spheres

55Q45

稳定球同伦

Stable homotopy of spheres

55Q50

J-[参见19L20]

J-morphism [See also 19L20]

55Q51

Vn周期性

Vn-periodicity

55Q52

特殊空间的同伦群

Homotopy groups of special spaces

55Q55

上同伦群

Cohomotopy groups

55Q70

特殊型同伦群[参见55N05, 55N07]

Homotopy groups of special types [See also 55N05, 55N07]

55Q91

等变化同伦群[参见19L47]

Equivariant homotopy groups [See also 19L47]

55Q99

其它

None of the above, but in this section

55Rxx

纤维空间和纤维丛[参见18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]

Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]

55R05

纤维空间

Fiber spaces

55R10

纤维丛

Fiber bundles

55R12

转移

Transfer

55R15

分类

Classification

55R20

纤维空间的谱序列和同调[参见55Txx]

Spectral sequences and homology of fiber spaces [See also 55Txx]

55R25

球丛和向量丛

Sphere bundles and vector bundles

55R35

群的分类空间和H-空间

Classifying spaces of groups and H-spaces

55R37

分类空间之间的映射

Maps between classifying spaces

55R40

分类空间的同调, 特征类[参见57Txx, 57R20]

Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]

55R45

BO, BU的同调和同伦; Bott周期性

Homology and homotopy of BO, and BU; Bott periodicity

55R50

向量空间丛的稳定类, K-理论[参见19Lxx](代数K-理论, 18F25, 19-XX)

Stable classes of vector space bundles, K-theory [See also 19Lxx] (For algebraic K-theory, see 18F25, 19-XX)

55R55

具有奇异性的纤维化

Fiberings with singularities

55R60

微丛和块丛[参见57N55, 57Q50]

Microbundles and block bundles [See also 57N55, 57Q50]

55R65

纤维空间和纤维丛的推广

Generalizations of fiber spaces and bundles

55R70

纤维式拓扑

Fibrewise topology

55R80

判别式簇, 构形空间

Discriminantal varieties, configuration spaces

55R91

等变化的纤维空间和纤维丛[参见19L47]

Equivariant fiber spaces and bundles [See also 19L47]

55R99

其它

None of the above, but in this section

55Sxx

运算和障碍

Operations and obstructions

55S05

一阶上同调运算

Primary cohomology operations

55S10

Steenrod代数

Steenrod algebra

55S12

Dyer-Lashof运算

Dyer-Lashof operations

55S15

对称积, 循环积

Symmetric products, cyclic products

55S20

二阶和高阶上同调运算

Secondary and higher cohomology operations

55S25

K-理论运算和广义上同调运算[参见19D55, 19Lxx]

K-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]

55S30

Massey

Massey products

55S35

障碍理论

Obstruction theory

55S36

映射的扩张和压缩

Extension and compression of mappings

55S37

映射的分类

Classification of mappings

55S40

分割纤维空间和纤维丛

Sectioning fiber spaces and bundles

55S45

Postnikov系统, k-不变式

Postnikov systems, k-invariants

55S91

等变化运算和障碍[参见19L47]

Equivariant operations and obstructions [See also 19L47]

55S99

其它

None of the above, but in this section

55Txx

谱序列[参见18G40, 55R20]

Spectral sequences [See also 18G40, 55R20]

55T05

一般理论

General

55T10

Serre谱序列

Serre spectral sequences

55T15

Adams谱序列

Adams spectral sequences

55T20

Eilenberg-Moore谱序列[参见57T35]

Eilenberg-Moore spectral sequences [See also 57T35]

55T25

广义上同调

Generalized cohomology

55T99

其它

None of the above, but in this section

55Uxx

应用同调代数和范畴论[参见18Gxx]

Applied homological algebra and category theory [See also 18Gxx]

55U05

抽象复形

Abstract complexes

55U10

单纯集和复形

Simplicial sets and complexes

55U15

链复形

Chain complexes

55U20

万有系数定理, Bockstein算子

Universal coefficient theorems, Bockstein operator

55U25

积的同调, Künneth公式

Homology of a product, Künneth formula

55U30

对偶性

Duality

55U35

抽象和公理同伦理论

Abstract and axiomatic homotopy theory

55U40

拓扑范畴, 同伦论的基础

Topological categories, foundations of homotopy theory

55U99

其它

None of the above, but in this section

57-XX

流形和胞腔复形(复流形, 32Qxx)

Manifolds and cell complexes (For complex manifolds, see 32Qxx)

57-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

57-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

57-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

57-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

57-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

57-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

57Mxx

低维拓扑

Low-dimensional topology

57M05

基本群, 表示, 自由微分演算

Fundamental group, presentations, free differential calculus

57M07

群论中的拓扑方法

Topological methods in group theory

57M10

覆盖空间

Covering spaces

57M12

特殊覆盖, 例如: 分枝覆盖

Special coverings, e.g. branched

57M15

与图论的关系[参见05Cxx]

Relations with graph theory [See also 05Cxx]

57M20

二维复形

Two-dimensional complexes

57M25

S3中的纽结和连接(高维, 57Q45)

Knots and links in S3 (For higher dimensions, see 57Q45)

57M27

纽结不变量和三维流形

Invariants of knots and 3-manifolds

57M30

病态纽结和曲面等, 病态嵌入

Wild knots and surfaces, etc., wild embeddings

57M35

Dehn引理, 球面定理, 圈定理, 非球面性

Dehn’s lemma, sphere theorem, loop theorem, asphericity

57M40

E3S3的特征(Poincaré猜想)[参见57N12]

Characterizations of E3 and S3 (Poincaré conjecture) [See also 57N12]

57M50

低维流形的几何结构

Geometric structures on low-dimensional manifolds

57M60

低维中的群作用

Group actions in low dimensions

57M99

其它

None of the above, but in this section

57Nxx

拓扑流形

Topological manifolds

57N05

E2的拓扑, 2维流形

Topology of E2, 2-manifolds

57N10

一般3维流形的拓扑[参见57Mxx]

Topology of general 3-manifolds [See also 57Mxx]

57N12

E3S3拓扑[参见57M40]

Topology of E3 and S3 [See also 57M40]

57N13

E4拓扑, 4维流形[参见14Jxx, 32Jxx]

Topology of E4, 4-manifolds [See also 14Jxx, 32Jxx]

57N15

En的拓扑, n-维流形(4<n<∞)

Topology of En, n-manifolds (4<n<∞)

57N16

流形上的几何结构[参见57M50]

Geometric structures on manifolds [See also 57M50]

57N17

拓扑向量空间的拓扑学

Topology of topological vector spaces

57N20

无限维流形的拓扑学[参见58Bxx]

Topology of infinite-dimensional manifolds [See also 58Bxx]

57N25

形状[参见54C56, 55P55, 55Q07]

Shapes [See also 54C56, 55P55, 55Q07]

57N30

淹没

Engulfing

57N35

嵌入和浸入

Embeddings and immersions

57N37

合痕和伪合痕

Isotopy and pseudo-isotopy

57N40

子流形的邻域

Neighborhoods of submanifolds

57N45

平坦性和驯顺性

Flatness and tameness

57N50

Sn-1En, Schoenflies问题

Sn-1En, Schoenflies problem

57N55

微丛和块丛[参见55R60, 57Q50]

Microbundles and block bundles [See also 55R60, 57Q50]

57N60

胞腔性

Cellularity

57N65

流形的代数拓扑

Algebraic topology of manifolds

57N70

配边与和谐性

Cobordism and concordance

57N75

一般位置和横截性

General position and transversality

57N80

层次

Stratifications

57N99

其它

None of the above, but in this section

57Pxx

广义流形[参见18F15]

Generalized manifolds [See also 18F15]

57P05

广义流形的局部性质

Local properties of generalized manifolds

57P10

Poincaré对偶性空间

Poincaré duality spaces

57P99

其它

None of the above, but in this section

57Qxx

PL-拓扑

PL-topology

57Q05

复形的一般拓扑

General topology of complexes

57Q10

单同调型、Whitehead挠率、Reidemeister-Franz挠率等[参见19B28]

Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]

57Q12

CW复形的Wall有限性障碍

Wall finiteness obstruction for CW-complexes

57Q15

三角剖分化流形

Triangulating manifolds

57Q20

配边

Cobordism

57Q25

PL结构的比较: 分类, Hauptver­mutung主要猜想

Comparison of PL-structures: classification, Hauptver­mutung

57Q30

淹没

Engulfing

57Q35

嵌入和浸入

Embeddings and immersions

57Q37

合痕

Isotopy

57Q40

正则邻域

Regular neighborhoods

57Q45

(高维中)纽结和连接(低维情形, 57M25)

Knots and links (in high dimensions) (For the low-dimensional case, see 57M25)

57Q50

微丛和块丛[参见55R60, 57N55]

Microbundles and block bundles [See also 55R60, 57N55]

57Q55

逼近

Approximations

57Q60

配边与和谐性

Cobordism and concordance

57Q65

一般位置和横截性

General position and transversality

57Q91

等变化的PL-拓扑

Equivariant PL-topology

57Q99

其它

None of the above, but in this section

57Rxx

微分拓扑(可微流形的基本问题, 58Axx; 无限维流形, 58Bxx)

Differential topology (For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimen­sional manifolds, see 58Bxx)

57R05

三角剖分

Triangulating

57R10

光滑性

Smoothing

57R12

光滑逼近

Smooth approximations

57R15

流形上的特定化结构(旋量流形、标架流形等)

Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)

57R17

辛拓扑和接触拓扑

Symplectic and contact topology

57R18

轨形拓扑和几何

Topology and geometry of orbifolds

57R19

流形上的代数拓扑

Algebraic topology on manifolds

57R20

示性类和示性数

Characteristic classes and numbers

57R22

向量丛拓扑和纤维丛拓扑[参见55Rxx]

Topology of vector bundles and fiber bundles [See also 55Rxx]

57R25

向量场, 标架场

Vector fields, frame fields

57R27

C实解析流形上的向量场的可控性[参见49Qxx, 37C10, 93B05]

Controllability of vector fields on C and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]

57R30

叶状结构物; 几何理论

Foliations; geometric theory

57R32

叶状结构物的分类空间; Gelfand-Fuks上同调[参见58H10]

Classifying spaces for foliations; Gelfand-Fuks cohomo­logy [See also 58H10]

57R35

可微映射

Differentiable mappings

57R40

嵌入

Embeddings

57R42

浸入

Immersions

57R45

可微映射的奇异性

Singularities of differentiable mappings

57R50

微分同胚

Diffeomorphisms

57R52

合痕

Isotopy

57R55

可微结构

Differentiable structures

57R56

拓扑量子场论

Topological quantum field theories

57R57

整体分析在流形、DonaldsonSeiberg-Witten不变量结构中的应用[参见58-XX]

Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

57R58

Floer()同调

Floer homology

57R60

同伦球面, Poincaré猜想

Homotopy spheres, Poincaré conjecture

57R65

换球术和环柄体

Surgery and handlebodies

57R67

换球术障碍, Wall[参见19J25]

Surgery obstructions, Wall groups [See also 19J25]

57R70

临界点和临界子流形

Critical points and critical submanifolds

57R75

O配边和SO配边

O- and SO-cobordism

57R77

复配边(U-配边和SU-配边)[参见55N22]

Complex cobordism (U- and SU-cobordism) [See also 55N22]

57R80

h-配边和s-配边

h- and s-cobordism

57R85

等变化配边

Equivariant cobordism

57R90

其它类型配边[参见55N22]

Other types of cobordism [See also 55N22]

57R91

流形的等变代数拓扑

Equivariant algebraic topology of manifolds

57R95

由子流形实现的循环

Realizing cycles by submanifolds

57R99

其它

None of the above, but in this section

57Sxx

拓扑变换群[参见20F34, 22-XX, 37-XX, 54H15, 58D05]

Topological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]

57S05

同胚或微分同胚群的拓扑性质

Topological properties of groups of homeomorphisms or diffeomorphisms

57S10

同胚的紧群

Compact groups of homeomorphisms

57S15

可微变换的紧Lie

Compact Lie groups of differentiable transformations

57S17

有限变换群

Finite transformation groups

57S20

变换非紧Lie

Noncompact Lie groups of transformations

57S25

作用在特殊流形上的群

Groups acting on specific manifolds

57S30

变换的不连续群

Discontinuous groups of transformations

57S99

其它

None of the above, but in this section

57Txx

拓扑群及相关结构的同调和同伦

Homology and homotopy of topological groups and related structures

57T05

Hopf代数[参见16T05]

Hopf algebras [See also 16T05]

57T10

Lie群的同调和上同调

Homology and cohomology of Lie groups

57T15

Lie群齐次空间的同调和上同调

Homology and cohomology of homogeneous spaces of Lie groups

57T20

拓扑群和齐次空间的同伦群

Homotopy groups of topological groups and homogeneous spaces

57T25

H-空间的同调和上同调

Homology and cohomology of H-spaces

57T30

带和同带构造[参见18G55, 55Uxx]

Bar and cobar constructions [See also 18G55, 55Uxx]

57T35

Eilenberg-Moore谱序列的应用[参见55R20, 55T20]

Applications of Eilenberg-Moore spectral sequences [See also 55R20, 55T20]

57T99

其它

None of the above, but in this section

58-XX

大范围分析, 流形上的分析[参见32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](几何积分理论, 49Q15)

Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] (For geometric integration theory, see 49Q15)

58-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

58-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

58-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

58-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

58-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

58-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

58Axx

可微流形的一般理论[参见32Cxx]

General theory of differentiable manifolds [See also 32Cxx]

58A03

Topos理论近似可微流形

Topos-theoretic approach to differentiable manifolds

58A05

可微流形, 基础

Differentiable manifolds, foundations

58A07

实解析流形和Nash流形[参见14P20, 32C07]

Real-analytic and Nash manifolds [See also 14P20, 32C07]

58A10

微分形式

Differential forms

58A12

de Rham理论[参见14Fxx]

de Rham theory [See also 14Fxx]

58A14

Hodge理论[参见14C30, 14Fxx, 32J25, 32S35]

Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]

58A15

外微分系统(Cartan理论)

Exterior differential systems (Cartan theory)

58A17

Pfaff系统

Pfaffian systems

58A20

射流

Jets

58A25

[参见32C30, 53C65]

Currents [See also 32C30, 53C65]

58A30

向量分布(切丛的子丛)

Vector distributions (subbundles of the tangent bundles)

58A32

自然丛

Natural bundles

58A35

分层集[参见32S60]

Stratified sets [See also 32S60]

58A40

微分空间

Differential spaces

58A50

超流形和分次流形[参见14A22, 32C11]

Supermanifolds and graded manifolds [See also 14A22, 32C11]

58A99

其它

None of the above, but in this section

58Bxx

无限维流形

Infinite-dimensional manifolds

58B05

同伦和拓扑问题

Homotopy and topological questions

58B10

可微性问题

Differentiability questions

58B12

全纯问题[参见32-XX, 46G20]

Questions of holomorphy [See also 32-XX, 46G20]

58B15

Fredholm结构[参见47A53]

Fredholm structures [See also 47A53]

58B20

Riemann, Finsler, 和其它几何结构[参见53C20, 53C60]

Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]

58B25

无限维流形上的群结构和推广[参见22E65, 58D05]

Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]

58B32

量子群的几何

Geometry of quantum groups

58B34

非交换几何(属于Connes)

Noncommutative geometry (à la Connes)

58B99

其它

None of the above, but in this section

58Cxx

流形上的微积分; 非线性算子[参见46Txx, 47Hxx, 47Jxx]

Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]

58C05

实值函数

Real-valued functions

58C06

集值映射和函数空间值映射[参见47H04, 54C60]

Set valued and function-space valued mappings [See also 47H04, 54C60]

58C07

映射的连续性性质

Continuity properties of mappings

58C10

全纯映射[参见32-XX]

Holomorphic maps [See also 32-XX]

58C15

隐函数定理; 整体Newton

Implicit function theorems; global Newton methods

58C20

微分法理论(GateauxFréchet)[参见26Exx, 46G05]

Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]

58C25

可微映射

Differentiable maps

58C30

流形上的不动点定理[参见47H10]

Fixed point theorems on manifolds [See also 47H10]

58C35

流形上的积分法; 流形上的测度[参见28Cxx]

Integration on manifolds; measures on manifolds [See also 28Cxx]

58C40

谱理论; 特征值问题[参见47J10, 58E07]

Spectral theory; eigenvalue problems [See also 47J10, 58E07]

58C50

超流形或分次流形上的分析

Analysis on supermanifolds or graded manifolds

58C99

其它

None of the above, but in this section

58Dxx

映射的空间和流形(包括46Exx的非线性形式)[参见46Txx, 53Cxx]

Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]

58D05

微分同胚群和作为流形的自同胚群[参见22E65, 57S05]

Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]

58D07

非线性算子的群和半群[参见17B65, 47H20]

Groups and semigroups of nonlinear operators [See also 17B65, 47H20]

58D10

嵌入和浸入的空间

Spaces of imbeddings and immersions

58D15

映射流形[参见46T10, 54C35]

Manifolds of mappings [See also 46T10, 54C35]

58D17

度量流形(特别是Riemann)

Manifolds of metrics (esp. Riemannian)

58D19

群的作用和对称性质

Group actions and symmetry properties

58D20

映射流形上的测度(Gauss的、圆柱形的等)[参见28Cxx, 46T12]

Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]

58D25

函数空间中的方程; 发展方程[参见34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]

Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]

58D27

微分几何结构的模问题

Moduli problems for differential geometric structures

58D29

拓扑结构的模问题

Moduli problems for topological structures

58D30

应用(在量子力学(Feynman路径积分)、相对性、流体动力学等)

Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)

58D99

其它

None of the above, but in this section

58Exx

无限维空间中的变分问题

Variational problems in infinite-dimensional spaces

58E05

抽象临界点理论(Morse理论、Ljusternik-Schnirelman (Lyus­ternik-Shnirelman)理论等)

Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)

58E07

抽象分歧理论

Abstract bifurcation theory

58E09

群不变分歧理论

Group-invariant bifurcation theory

58E10

应用于测地线的理论(单独立变量问题)

Applications to the theory of geodesics (problems in one independent variable)

58E11

临界度量

Critical metrics

58E12

应用于极小曲面(双独立变量问题)[参见49Q05]

Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]

58E15

应用于多变量极值问题; Yang-Mills泛函[参见81T13]

Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.

58E17

Pareto最优性等, 经济学中的应用[参见90C29]

Pareto optimality, etc., applications to economics [See also 90C29]

58E20

调和映射[参见53C43]

Harmonic maps [See also 53C43], etc.

58E25

控制论中的应用[参见49-XX, 93-XX]

Applications to control theory [See also 49-XX, 93-XX]

58E30

变分原理

Variational principles

58E35

变分不等式(整体问题)

Variational inequalities (global problems)

58E40

群的作用

Group actions

58E50

应用

Applications

58E99

其它

None of the above, but in this section

58Hxx

流形上的伪群, 可微广群和一般结构

Pseudogroups, differentiable groupoids and general structures on manifolds


58H05

伪群和可微广群[参见22A22, 22E65]

Pseudogroups and differentiable groupoids [See also 22A22, 22E65]

58H10

伪群结构(SpencerGelfand-Fuks)分类空间的上同调[参见57R32]

Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]

58H15

结构的形变[参见32Gxx, 58J10]

Deformations of structures [See also 32Gxx, 58J10]

58H99

其它

None of the above, but in this section

58Jxx

流形上的偏微分方程; 微分算子[参见32Wxx, 35-XX, 53Cxx]

Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]

58J05

流形上的椭圆型方程, 一般理论[参见35-XX]

Elliptic equations on manifolds, general theory [See also 35-XX]

58J10

微分复形[参见35Nxx]; 椭圆复形

Differential complexes [See also 35Nxx]; elliptic complexes

58J15

与超函数的关系

Relations with hyperfunctions

58J20

指数理论及相关的不动点定理[参见19K56, 46L80]

Index theory and related fixed point theorems [See also 19K56, 46L80]

58J22

异种指数理论[参见19K56, 46L05, 46L10, 46L80, 46M20]

Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]

58J26

椭圆亏格

Elliptic genera

58J28

Eta-不变量, Chern-Simons不变量

Eta-invariants, Chern-Simons invariants

58J30

谱流

Spectral flows

58J32

流形上的边值问题

Boundary value problems on manifolds

58J35

热和其它抛物型方程方法

Heat and other parabolic equation methods

58J37

摄动; 渐近性

Perturbations; asymptotics

58J40

流形上的伪微分和Fourier积分算子[参见35Sxx]

Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]

58J42

非交换整体分析, 非交换剩余

Noncommutative global analysis, noncommutative residues

58J45

双曲型方程[参见35Lxx]

Hyperbolic equations [See also 35Lxx]

58J47

奇异性传播; 初值问题

Propagation of singularities; initial value problems

58J50

谱问题; 谱几何; 散射理论[参见35Pxx]

Spectral problems; spectral geometry; scattering theory [See also 35Pxx]

58J51

谱理论和遍历理论之间的关系, 例如: 量子唯一遍历性

Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity

58J52

行列式和行列式丛, 解析挠率

Determinants and determinant bundles, analytic torsion

58J53

等谱性

Isospectrality

58J55

分歧[参见35B32]

Bifurcation [See also 35B32]

58J60

与特殊流形结构的关系(RiemannFinsler)

Relations with special manifold structures (Riemannian, Finsler, etc.)

58J65

流形上的扩散过程和随机分析[参见35R60, 60H10, 60J60]

Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

58J70

不变性和对称性质[参见35A30]

Invariance and symmetry properties [See also 35A30]

58J72

对应和其它变换方法(例如: Lie-Bäcklund)[参见35A22]

Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]

58J90

应用

Applications

58J99

其它

None of the above, but in this section

58Kxx

奇异性理论和突变理论[参见32Sxx, 37-XX]

Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]

58K05

函数和映射的临界点

Critical points of functions and mappings

58K10

单值[]

Monodromy

58K15

映射的拓扑性质

Topological properties of mappings

58K20

映射的代数和解析性质

Algebraic and analytic properties of mappings

58K25

稳定性

Stability

58K30

全局理论

Global theory

58K35

突变理论

Catastrophe theory

58K40

分类; 映射芽的有限确定性

Classification; finite determinacy of map germs

58K45

向量场的奇异性, 拓扑方面

Singularities of vector fields, topological aspects

58K50

标准型

Normal forms

58K55

渐近性态

Asymptotic behavior

58K60

奇异性的变形

Deformation of singularities

58K65

拓扑不变量

Topological invariants

58K70

对称性, 同变性

Symmetries, equivariance

58K99

其它

None of the above, but in this section

58Zxx

在物理上的应用

Applications to physics

58Z05

在物理上的应用

Applications to physics

58Z99

其它

None of the above, but in this section

60-XX

概率论和随机过程(其它应用, 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)

Probability theory and stochastic pro­cesses (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)

60-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

60-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

60-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

60-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

60-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

60-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

60-08

计算方法(在更特殊等级上不分类)[参见65C50]

Computational methods (not classified at a more specific level) [See also 65C50]

60Axx

概率论基础

Foundations of probability theory

60A05

公理; 其它一般问题

Axioms; other general questions

60A10

概率测度论(遍历理论, 28Dxx60Fxx)

Probabilistic measure theory (For ergodic theory, see 28Dxx and 60Fxx)

60A86

模糊概率

Fuzzy probability

60A99

其它

None of the above, but in this section

60Bxx

代数结构和拓扑结构上的概率论

Probability theory on algebraic and topological structures

60B05

拓扑空间上的概率测度

Probability measures on topological spaces

60B10

概率测度的收敛性

Convergence of probability measures

60B11

线性拓扑空间上的概率理论[参见28C20]

Probability theory on linear topological spaces [See also 28C20]

60B12

向量值随机变量的极限定理(无限维情形)

Limit theorems for vector-valued random variables (infinite-dimensional case)

60B15

群或半群、Fourier变换、因子分解上的概率测度

Probability measures on groups or semigroups, Fourier transforms, factorization

60B20

随机矩阵(概率方面; 代数方面见15B52)

Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

60B99

其它

None of the above, but in this section

60Cxx

组合概率

Combinatorial probability

60C05

组合概率

Combinatorial probability

60C99

其它

None of the above, but in this section

60Dxx

几何概率和随机几何[参见52A22, 53C65]

Geometric probability and stochastic geometry [See also 52A22, 53C65]

60D05

几何概率和随机几何[参见52A22, 53C65]

Geometric probability and stochastic geometry [See also 52A22, 53C65]

60D99

其它

None of the above, but in this section

60Exx

分布论[参见62Exx, 62Hxx]

Distribution theory [See also 62Exx, 62Hxx]

60E05

分布: 一般理论

Distributions: general theory

60E07

无限可分分布; 稳定分布

Infinitely divisible distributions; stable distributions

60E10

特征函数; 其它变换

Characteristic functions; other transforms

60E15

不等式; 随机序

Inequalities; stochastic orderings

60E99

其它

None of the above, but in this section

60Fxx

极限定理[参见28Dxx, 60B12]

Limit theorems [See also 28Dxx, 60B12]

60F05

中心极限定理和其它弱定理

Central limit and other weak theorems

60F10

大偏差

Large deviations

60F15

强定理

Strong theorems

60F17

泛函极限定理; 不变性原理

Functional limit theorems; invariance principles

60F20

0-1定律

Zero-one laws

60F25

Lp-限定理

Lp-limit theorems

60F99

其它

None of the above, but in this section

60Gxx

随机过程

Stochastic processes

60G05

随机过程的基础

Foundations of stochastic processes

60G07

过程的一般理论

General theory of processes

60G09

可交换性

Exchangeability

60G10

平稳过程

Stationary processes

60G12

一般二阶过程

General second-order processes

60G15

Gauss过程

Gaussian processes

60G17

样本道路性质

Sample path properties

60G18

自相似过程

Self-similar processes

60G20

广义随机过程

Generalized stochastic processes

60G22

分式过程, 包括分式Brown运动

Fractional processes, including fractional Brownian motion

60G25

预报理论[参见62M20]

Prediction theory [See also 62M20]

60G30

诱导测度的连续性和奇异性

Continuity and singularity of induced measures

60G35

信号检测和滤波[参见62M20, 93E10, 93E11, 94Axx]

Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

60G40

停止时间; 最优停止问题; 博弈论[参见62L15, 91A60]

Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

60G42

离散参数的鞅

Martingales with discrete parameter

60G44

连续参数的鞅

Martingales with continuous parameter

60G46

鞅和经典分析

Martingales and classical analysis

60G48

鞅的推广

Generalizations of martingales

60G50

独立随机变量的和; 随机游动

Sums of independent random variables; random walks

60G51

独立增量过程; Lévy过程

Processes with independent increments; Lévy processes

60G52

稳定过程

Stable processes

60G55

点过程

Point processes

60G57

随机测度

Random measures

60G60

随机场

Random fields

60G70

极值理论; 极值过程

Extreme value theory; extremal processes

60G99

其它

None of the above, but in this section

60Hxx

随机分析[参见58J65]

Stochastic analysis [See also 58J65]

60H05

随机积分

Stochastic integrals

60H07

变分随机微积分和Malliavin微积分

Stochastic calculus of variations and the Malliavin calculus

60H10

随机常微分方程[参见34F05]

Stochastic ordinary differential equations [See also 34F05]

60H15

随机偏微分方程[参见35R60]

Stochastic partial differential equations [See also 35R60]

60H20

随机积分方程

Stochastic integral equations

60H25

随机算子和方程[参见47B80]

Random operators and equations [See also 47B80]

60H30

随机分析的应用(偏微分方程等)

Applications of stochastic analysis (to PDE, etc.)

60H35

随机方程的计算方法[参见65C30]

Computational methods for stochastic equations [See also 65C30]

60H40

白噪声理论

White noise theory

60H99

其它

None of the above, but in this section

60Jxx

Markov过程

Markov processes

60J05

一般状态空间上离散时间Markov过程

Discrete-time Markov processes on general state spaces

60J10

Markov(离散状态空间上离散时间Markov过程)

Markov chains (discrete-time Markov processes on discrete state spaces)

60J20

一般状态空间上Markov链和离散时间Markov过程的应用(社会迁移率、学习理论、工业过程等)[参见90B30, 91D10, 91D35, 91E40]

Applications of Markov chains and discrete-time Markov processes on general state spaces(social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]

60J22

Markov链中的计算方法[参见65C40]

Computational methods in Markov chains [See also 65C40]

60J25

一般状态空间上连续时间Markov过程

Continuous-time Markov processes on general state spaces

60J27

离散状态空间上连续时间Markov过程

Continuous-time Markov processes on discrete state spaces

60J28

离散状态空间上连续时间Markov过程的应用

Applications of continuous-time Markov processes on discrete state spaces

60J35

转移函数, 生成元和预解式[参见47D03, 47D07]

Transition functions, generators and resolvents [See also 47D03, 47D07]

60J40

右过程

Right processes

60J45

概率位势论[参见31Cxx, 31D05]

Probabilistic potential theory [See also 31Cxx, 31D05]

60J50

边界理论

Boundary theory

60J55

局部时间和加性泛函

Local time and additive functionals

60J57

乘性泛函

Multiplicative functionals

60J60

扩散过程[参见58J65]

Diffusion processes [See also 58J65]

60J65

Brown运动[参见58J65]

Brownian motion [See also 58J65]

60J67

随机(Schramm-)Loewner进化(SLE)

Stochastic (Schramm-Loewner evolution (SLE)

60J68

超过程

Superprocesses

60J70

Brown运动和扩散理论的应用(人口遗传学、吸收问题等)[参见92Dxx]

Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

60J75

跳跃过程

Jump processes

60J80

分枝过程(Galton-Waston过程、生灭过程等)

Branching processes (Galton-Watson, birth-and-death, etc.)

60J85

分枝过程的应用[参见92Dxx]

Applications of branching processes [See also 92Dxx]

60J99

其它

None of the above, but in this section

60Kxx

特殊过程

Special processes

60K05

更新理论

Renewal theory

60K10

应用(可靠性、需求理论等)

Applications (reliability, demand theory, etc.)

60K15

Markov更新过程, Markov过程

Markov renewal processes, semi-Markov processes

60K20

Markov更新过程的应用(可靠性、排队网络等)[参见90Bxx]

Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]

60K25

排队论[参见68M20, 90B22]

Queueing theory [See also 68M20, 90B22]

60K30

应用(密集、配置、存贮、交通等)[参见90Bxx]

Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]

60K35

交互作用随机过程; 统计力学型模型; 渗透理论[参见82B43, 82C43]

Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

60K37

随机环境中的过程

Processes in random environments

60K40

随机过程的其它物理应用

Other physical applications of random processes

60K99

其它

None of the above, but in this section

62-XX

统计学

Statistics

62-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

62-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

62-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

62-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

62-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

62-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

62-07

数据分析

Data analysis

62-09

图解法

Graphical methods

62Axx

基础和哲学论题

Foundational and philosophical topics

62A01

基础和哲学论题

Foundational and philosophical topics

62A86

统计学中的模糊分析

Fuzzy analysis in statistics

62A99

其它

None of the above, but in this section

62Bxx

充分性和信息

Sufficiency and information

62B05

充分统计学和域

Sufficient statistics and fields

62B10

信息论课题[参见94A17]

Information-theoretic topics [See also 94A17]

62B15

统计实验的理论

Theory of statistical experiments

62B86

模糊性, 充分性和信息

Fuzziness, sufficiency, and information

62B99

其它

None of the above, but in this section

62Cxx

决策理论[参见90B50, 91B06](对策论, 91A35)

Decision theory [See also 90B50, 91B06] (For game theory, see 91A35)

62C05

一般考虑

General considerations

62C07

完全类结果

Complete class results

62C10

Bayes问题; Bayes方法的特性

Bayesian problems; characterization of Bayes procedures

62C12

经验决策方法; 经验Bayes方法

Empirical decision procedures; empirical Bayes procedures

62C15

容许性

Admissibility

62C20

极大极小方法

Minimax procedures

62C25

复合决策问题

Compound decision problems

62C86

决策论与模糊性

Decision theory and fuzziness

62C99

其它

None of the above, but in this section

62Dxx

抽样理论, 样本调查

Sampling theory, sample surveys

62D05

抽样理论, 样本调查

Sampling theory, sample surveys

62D99

其它

None of the above, but in this section

62Exx

分布论[参见60Exx]

Distribution theory [See also 60Exx]

62E10

特征和结构理论

Characterization and structure theory

62E15

精确分布论

Exact distribution theory

62E17

分布近似(非渐近)

Approximations to distributions (nonasymptotic)

62E20

渐近分布论

Asymptotic distribution theory

62E86

本节中与分布主题相关的模糊性

Fuzziness in connection with the topics on distributions in this section

62E99

其它

None of the above, but in this section

62Fxx

参数推断

Parametric inference

62F03

假设检验

Hypothesis testing

62F05

检验的渐近性质

Asymptotic properties of tests

62F07

秩评定和选择

Ranking and selection

62F10

点估计

Point estimation

62F12

估计量的渐近性质

Asymptotic properties of estimators

62F15

Bayes推断

Bayesian inference

62F25

容许区域和置信区域

Tolerance and confidence regions

62F30

约束下的推断

Inference under constraints

62F35

稳健性和自适应过程

Robustness and adaptive procedures

62F40

自助法、刀切法和其它再抽样法

Bootstrap, jackknife and other resampling methods

62F86

参数推断和模糊性

Parametric inference and fuzziness

62F99

其它

None of the above, but in this section

62Gxx

非参数推断

Nonparametric inference

62G05

估计

Estimation

62G07

密度估计

Density estimation

62G08

非参数回归

Nonparametric regression

62G09

再抽样法

Resampling methods

62G10

假设检验

Hypothesis testing

62G15

容许区域和置信区域

Tolerance and confidence regions

62G20

渐近性质

Asymptotic properties

62G30

顺序统计学; 经验分布函数

Order statistics; empirical distribution functions

62G32

极值统计学; 尾推论

Statistics of extreme values; tail inference

62G35

稳健性

Robustness

62G86

非参数推断和模糊性

Nonparametric inference and fuzziness

62G99

其它

None of the above, but in this section

62Hxx

多元分析[参见60Exx]

Multivariate analysis [See also 60Exx]

62H05

特征和结构理论

Characterization and structure theory

62H10

统计分布

Distribution of statistics

62H11

方向数据; 空间统计学

Directional data; spatial statistics

62H12

估计

Estimation

62H15

假设检验

Hypothesis testing

62H17

列联表

Contingency tables

62H20

结合(相关、标准相关等)的测度

Measures of association (correlation, canonical correlation, etc.)

62H25

因子分析和主分量; 对应分析

Factor analysis and principal components; correspondence analysis

62H30

分类和判别; 聚类分析[参见68T10, 91C20]

Classification and discrimination; cluster analysis [See also 68T10, 91C20]

62H35

图像分析

Image analysis

62H86

多元分析和模糊性

Multivariate analysis and fuzziness

62H99

其它

None of the above, but in this section

62Jxx

线性推断, 回归

Linear inference, regression

62J02

一般非线性回归

General nonlinear regression

62J05

线性回归

Linear regression

62J07

岭回归; 收缩估计量

Ridge regression; shrinkage estimators

62J10

方差和协方差分析

Analysis of variance and covariance

62J12

广义线性模型

Generalized linear models

62J15

成对和多重比较

Paired and multiple comparisons

62J20

诊断学

Diagnostics

62J86

模糊性, 线性推断和回归

Fuzziness, and linear inference and regression

62J99

其它

None of the above, but in this section

62Kxx

实验设计[参见05Bxx]

Design of experiments [See also 05Bxx]

62K05

最优设计

Optimal designs

62K10

区组设计

Block designs

62K15

析因设计

Factorial designs

62K20

响应曲面设计

Response surface designs

62K25

稳健参数设计

Robust parameter designs

62K86

实验的模糊性和设计

Fuzziness and design of experiments

62K99

其它

None of the above, but in this section

62Lxx

序贯法

Sequential methods

62L05

序贯设计

Sequential design

62L10

序贯分析

Sequential analysis

62L12

序贯估计

Sequential estimation

62L15

最优停止[参见60G40, 91A60]

Optimal stopping [See also 60G40, 91A60]

62L20

随机逼近

Stochastic approximation

62L86

模糊性和序贯法

Fuzziness and sequential methods

62L99

其它

None of the above, but in this section

62Mxx

随机过程推断

Inference from stochastic processes

62M02

Markov过程: 假设检验

Markov processes: hypothesis testing

62M05

Markov过程: 估计

Markov processes: estimation

62M07

Markov过程: 假设检验

Non-Markovian processes: hypothesis testing

62M09

Markov过程: 估计

Non-Markovian processes: estimation

62M10

时间序列、自动相关、回归等[参见91B84]

Time series, auto-correlation, regression, etc. [See also 91B84]

62M15

谱分析

Spectral analysis

62M20

预报[参见60G25]; 滤波[参见60G35, 93E10, 93E11]

Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

62M30

空间过程

Spatial processes

62M40

随机场; 图象分析

Random fields; image analysis

62M45

神经网及相关方法

Neural nets and related approaches

62M86

来自随机过程和模糊性的推断

Inference from stochastic processes and fuzziness

62M99

其它

None of the above, but in this section

62Nxx

生存分析和截尾数据

Survival analysis and censored data

62N01

截尾数据模型

Censored data models

62N02

估计

Estimation

62N03

检验

Testing

62N05

可靠性和寿命试验[参见90B25]

Reliability and life testing [See also 90B25]

62N86

模糊性, 生存分析和截尾数据

Fuzziness, and survival analysis and censored data

62N99

其它

None of the above, but in this section

62Pxx

应用[参见90-XX, 91-XX, 92-XX]

Applications [See also 90-XX, 91-XX, 92-XX]

62P05

在精算学和金融数学的应用

Applications to actuarial sciences and financial mathematics

62P10

在生物学和医学科学的应用

Applications to biology and medical sciences

62P12

应用于环境及相关课题

Applications to environmental and related topics

62P15

在心理学方面的应用

Applications to psychology

62P20

在经济学方面的应用[参见91Bxx]

Applications to economics [See also 91Bxx]

62P25

在社会科学方面的应用

Applications to social sciences

62P30

应用于工程和工业

Applications in engineering and industry

62P35

应用于物理

Applications to physics

62P99

其它

None of the above, but in this section

62Qxx

统计表

Statistical tables

62Q05

统计表

Statistical tables

62Q99

其它

None of the above, but in this section

65-XX

数值分析

Numerical analysis

65-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

65-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

65-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

65-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

65-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

65-05

实验论文

Experimental papers

65-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

65Axx

Tables

65A05

Tables

65A99

其它

None of the above, but in this section

65Bxx

收敛性的加速

Acceleration of convergence

65B05

极限外推, 延迟校正

Extrapolation to the limit, deferred corrections

65B10

级数求和

Summation of series

65B15

Euler-Maclaurin公式

Euler-Maclaurin formula

65B99

其它

None of the above, but in this section

65Cxx

概率方法, 模拟和随机微分方程(理论方面, 68U2060H35)

Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35)

65C05

Monte Carlo方法

Monte Carlo methods

65C10

随机数生成

Random number generation

65C20

模型, 数值方法[参见68U20]

Models, numerical methods [See also 68U20]

65C30

随机微分和积分方程

Stochastic differential and integral equations

65C35

随机粒子法[参见82C80]

Stochastic particle methods [See also 82C80]

65C40

计算Markov

Computational Markov chains

65C50

概率中的其它计算问题

Other computational problems in probability

65C60

统计学中的计算问题

Computational problems in statistics

65C99

其它

None of the above, but in this section

65Dxx

数值逼近和计算几何(基本算法)(理论, 41-XX68Uxx)

Numerical approximation and computational geometry (Primarily algorithms) (for theory, see 41-XX and 68Uxx)

65D05

插值

Interpolation

65D07

样条

Splines

65D10

光滑, 曲线拟合

Smoothing, curve fitting

65D15

函数逼近算法

Algorithms for functional approximation

65D17

计算机辅助设计(曲线和曲面的模型建立)[参见68U07]

Computer aided design (modeling of curves and surfaces) [See also 68U07]

65D18

计算机图形学, 图象分析和计算几何[参见51N05, 68U05]

Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05]

65D19

计算机中计算问题和机器人视觉

Computational issues in computer and robotic vision

65D20

特殊函数的计算, 表的构造[参见33F05]

Computation of special functions, construction of tables [See also 33F05]

65D25

数值微分法

Numerical differentiation

65D30

数值积分法

Numerical integration

65D32

求面积和体积公式

Quadrature and cubature formulas

65D99

其它

None of the above, but in this section

65Exx

复分析中的数值方法(位势论等)[共形映射的数值方法, 参见30C30]

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30]

65E05

复分析中的数值方法(位势论等)[共形映射的数值方法, 参见30C30]

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30]

65E99

其它

None of the above, but in this section

65Fxx

数值线性代数

Numerical linear algebra

65F05

线性系统和矩阵反演的直接法

Direct methods for linear systems and matrix inversion

65F08

迭代法的预条件子

Preconditioners for iterative methods

65F10

线性系统的迭代法[参见65N22]

Iterative methods for linear systems [See also 65N22]

65F15

特征值, 特征向量

Eigenvalues, eigenvectors

65F18

逆特征值问题

Inverse eigenvalue problems

65F20

超定组, 伪逆

Overdetermined systems, pseudoinverses

65F22

不适定性, 正则化

Ill-posedness, regularization

65F25

正交化

Orthogonalization

65F30

其它矩阵算法

Other matrix algorithms

65F35

矩阵范数, 条件作用, 比例[参见15A12, 15A60]

Matrix norms, conditioning, scaling [See also 15A12, 15A60]

65F40

行列式

Determinants

65F50

稀疏矩阵

Sparse matrices

65F60

矩阵指数和相似矩阵函数

Matrix exponential and similar matrix functions

65F99

其它

None of the above, but in this section

65Gxx

误差分析和区间分析

Error analysis and interval analysis

65G20

自动结果验证算法

Algorithms with automatic result verification

65G30

区间和有限算术

Interval and finite arithmetic

65G40

区间分析中的一般方法

General methods in interval analysis

65G50

舍入误差

Roundoff error

65G99

其它

None of the above, but in this section

65Hxx

非线性代数方程或超越方程

Nonlinear algebraic or transcendental equations

65H04

多项式方程的根

Roots of polynomial equations

65H05

单一方程

Single equations

65H10

方程组

Systems of equations

65H17

特征值, 特征向量[参见47Hxx, 47Jxx, 58C40, 58E07, 90C30]

Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30]

65H20

整体方法, 包括同伦法[参见58C30, 90C30]

Global methods, including homotopy approaches [See also 58C30, 90C30]

65H99

其它

None of the above, but in this section

65Jxx

抽象空间中的数值分析

Numerical analysis in abstract spaces

65J05

一般理论

General theory

65J08

抽象发展方程

Abstract evolution equations

65J10

线性算子方程(不用65Fxx)

Equations with linear operators (do not use 65Fxx)

65J15

非线性算子方程(不用65Hxx)

Equations with nonlinear operators (do not use 65Hxx)

65J20

不适定的问题; 正则化

Improperly posed problems; regularization

65J22

逆问题

Inverse problems

65J99

其它

None of the above, but in this section

65Kxx

数学规划, 最优化和变分法

Mathematical programming, optimization and variational techniques

65K05

数学规划法[参见90Cxx]

Mathematical programming methods [See also 90Cxx]

65K10

最优化和变分法[参见49Mxx, 93B40]

Optimization and variational techniques [See also 49Mxx, 93B40]

65K15

变分不等式及相关问题的数值方法

Numerical methods for variational inequalities and related problems

65K99

其它

None of the above, but in this section

65Lxx

常微分方程

Ordinary differential equations

65L03

泛函微分方程

Functional-differential equations

65L04

刚性方程

Stiff equations

65L05

初值问题

Initial value problems

65L06

多步法, Runge-Kutta法和外推法

Multistep, Runge-Kutta and extrapolation methods

65L07

解稳定性的数值研究

Numerical investigation of stability of solutions

65L08

不适定问题

Improperly posed problems

65L09

逆问题

Inverse problems

65L10

边值问题

Boundary value problems

65L11

奇异摄动问题

Singularly perturbed problems

65L12

有限差分法

Finite difference methods

65L15

特征值问题

Eigenvalue problems

65L20

数值方法的稳定性和收敛性

Stability and convergence of numerical methods

65L50

网格生成和加细

Mesh generation and refinement

65L60

有限元法, Rayleigh-Ritz, Galerkin法和配置法

Finite elements, Rayleigh-Ritz, Galerkin and collocation methods

65L70

误差界

Error bounds

65L80

微分-代数方程的方法

Methods for differential-algebraic equations

65L99

其它

None of the above, but in this section

65Mxx

偏微分方程, 初值和不定常的初-边值问题

Partial differential equations, initial value and time-dependent initial-boundary value problems

65M06

有限差分法

Finite difference methods

65M08

有限体积法

Finite volume methods

65M12

数值方法的稳定性和收敛性

Stability and convergence of numerical methods

65M15

误差界

Error bounds

65M20

线方法

Method of lines

65M22

离散方程的解[参见65Fxx, 65Hxx]

Solution of discretized equations [See also 65Fxx, 65Hxx]

65M25

特征法

Method of characteristics

65M30

不适定问题

Improperly posed problems

65M32

逆问题

Inverse problems

65M38

边界元法

Boundary element methods

65M50

网格生成和加细

Mesh generation and refinement

65M55

多重网格法; 区域分解

Multigrid methods; domain decomposition

65M60

有限元法, Rayleigh-Ritz法和Galerkin, 有限法

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

65M70

谱方法, 配置和相关方法

Spectral, collocation and related methods

65M75

概率方法、粒子法等

Probabilistic methods, particle methods, etc.

65M80

基本解、Green函数法等

Fundamental solutions, Green’s function methods, etc.

65M85

虚构区域法

Fictitious domain methods

65M99

其它

None of the above, but in this section

65Nxx

偏微分方程, 边值问题

Partial differential equations, boundary value problems

65N06

有限差分法

Finite difference methods

65N08

有限体积法

Finite volume methods

65N12

数值方法的稳定性和收敛性

Stability and convergence of numerical methods

65N15

误差界

Error bounds

65N20

不适定问题

Ill-posed problems

65N21

逆问题

Inverse problems

65N22

离散方程的解[参见65Fxx, 65Hxx]

Solution of discretized equations [See also 65Fxx, 65Hxx]

65N25

特征值问题

Eigenvalue problems

65N30

有限元法, Rayleigh-Ritz法和Galerkin, 有限法

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

65N35

谱方法, 配置和相关方法

Spectral, collocation and related methods

65N38

边界元法

Boundary element methods

65N40

线方法

Method of lines

65N45

边界收缩法

Method of contraction of the boundary

65N50

网格生成和加细

Mesh generation and refinement

65N55

多重网格法; 区域分解

Multigrid methods; domain decomposition

65N75

概率方法、粒子法等

Probabilistic methods, particle methods, etc.

65N80

基本解、Green函数法等

Fundamental solutions, Green’s function methods, etc.

65N85

虚构区域法

Fictitious domain methods

65N99

其它

None of the above, but in this section

65Pxx

动力系统中的数值问题[参见37Mxx]

Numerical problems in dynamical systems [See also 37Mxx]

65P10

包括辛积分器的Hamilton系统

Hamiltonian systems including symplectic integrators

65P20

数值混沌

Numerical chaos

65P30

分歧问题

Bifurcation problems

65P40

非线性稳定性

Nonlinear stabilities

65P99

其它

None of the above, but in this section

65Qxx

差分和泛函方程, 递推关系

Difference and functional equations, recurrence relations

65Q10

差分方程

Difference equations

65Q20

泛函方程

Functional equations

65Q30

递推关系

Recurrence relations

65Q99

其它

None of the above, but in this section

65Rxx

积分方程, 积分变换

Integral equations, integral transforms

65R10

积分变换

Integral transforms

65R20

积分方程

Integral equations

65R30

不适定问题

Improperly posed problems

65R32

逆问题

Inverse problems

65R99

其它

None of the above, but in this section

65Sxx

图解法

Graphical methods

65S05

图解法

Graphical methods

65S99

其它

None of the above, but in this section

65Txx

Fourier分析中的数值方法

Numerical methods in Fourier analysis

65T40

三角逼近和插值

Trigonometric approximation and interpolation

65T50

离散和快速Fourier变换

Discrete and fast Fourier transforms

65T60

小波

Wavelets

65T99

其它

None of the above, but in this section

65Yxx

数值算法的计算机方面

Computer aspects of numerical algorithms

65Y04

计算机运算的算法等[参见68M07]

Algorithms for computer arithmetic, etc. [See also 68M07]

65Y05

并行计算

Parallel computation

65Y10

具体结构类算法

Algorithms for specific classes of architectures

65Y15

软件包方法

Packaged methods

65Y20

数值算法的复杂性和性能[参见68Q25]

Complexity and performance of numerical algorithms [See also 68Q25]

65Y99

其它

None of the above, but in this section

65Zxx

应用于物理

Applications to physics

65Z05

应用于物理

Applications to physics

65Z99

其它

None of the above, but in this section

68-XX

计算机科学(特殊数学领域中涉及机器计算和程序的论文, 见有关领域-04部分)

Computer science (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)

68-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

68-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

68-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

68-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

68-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

68-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

68Mxx

计算机系统结构

Computer system organization

68M01

一般理论

General

68M07

计算机体系结构的数学问题

Mathematical problems of computer architecture

68M10

网络设计和通信[参见68R10, 90B18]

Network design and communication [See also 68R10, 90B18]

68M11

与互联网相关的议题[参见68U35]

Internet topics [See also 68U35]

68M12

网络协议

Network protocols

68M14

分布系统

Distributed systems

68M15

可靠性, 检测和容错[参见94C12]

Reliability, testing and fault tolerance [See also 94C12]

68M20

性能评估; 排队; 调度[参见60K25, 90Bxx]

Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

68M99

其它

None of the above, but in this section

68Nxx

软件

Software

68N01

一般理论

General

68N15

程序设计语言

Programming languages

68N17

逻辑程序设计

Logic programming

68N18

功能程序设计和λ演算[参见03B40]

Functional programming and lambda calculus [See also 03B40]

68N19

其它程序设计技术(面向对象、顺序的、并行的、自动的等)

Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)

68N20

编译程序和解释程序

Compilers and interpreters

68N25

操作系统

Operating systems

68N30

软件工程的数学方面(规格、检验、度量、需求等)

Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)

68N99

其它

None of the above, but in this section

68Pxx

数据理论

Theory of data

68P01

一般理论

General

68P05

数据结构

Data structures

68P10

搜索和分类

Searching and sorting

68P15

数据库理论

Database theory

68P20

信息存储和检索

Information storage and retrieval

68P25

数据加密[参见94A60, 81P94]

Data encryption [See also 94A60, 81P94]

68P30

编码和信息理论(通信压缩、通信紧致、通信模型、编码方案等)[参见94Axx]

Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]

68P99

其它

None of the above, but in this section

68Qxx

计算理论

Theory of computing

68Q01

一般理论

General

68Q05

计算模型(Turing机等)[参见03D10, 68Q12, 81P68]

Models of computation (Turing machines, etc.) [See also 03D10, 68Q12, 81P68]

68Q10

计算模式(非确定性、并行的、交互的、概率的等)[参见68Q85]

Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]

68Q12

量子算法与复杂性[参见68Q05, 81P68]

Quantum algorithms and complexity [See also 68Q05, 81P68]

68Q15

复杂性类别(分层、复杂性类别中的关系等)[参见03D15, 68Q17, 68Q19]

Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]

68Q17

计算问题的难度(下界、完全性、逼近的难度等)[参见68Q15]

Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]

68Q19

描述复杂性和有限模型[参见03C13]

Descriptive complexity and finite models [See also 03C13]

68Q25

算法分析和问题复杂性[参见68W40]

Analysis of algorithms and problem complexity [See also 68W40]

68Q30

算法信息理论(Kolmogorov复杂性等)[参见03D32]

Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]

68Q32

计算学习理论[参见68T05]

Computational learning theory [See also 68T05]

68Q42

文法和重写系统

Grammars and rewriting systems

68Q45

形式语言和自动机[参见03D05, 68Q70, 94A45]

Formal languages and automata [See also 03D05, 68Q70, 94A45]

68Q55

语义学[参见03B70, 06B35, 18C50]

Semantics [See also 03B70, 06B35, 18C50]

68Q60

说明和检验(程序逻辑、模型校验等)[参见03B70]

Specification and verification (program logics, model checking, etc.) [See also 03B70]

68Q65

抽象数据类型; 代数说明[参见18C50]

Abstract data types; algebraic specification [See also 18C50]

68Q70

语言和自动机的代数理论[参见18B20, 20M35]

Algebraic theory of languages and automata [See also 18B20, 20M35]

68Q80

细胞自动机[参见37B15]

Cellular automata [See also 37B15]

68Q85

并行和分布计算的模型和方法(进程代数、双模拟、转移网等)

Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)

68Q87

计算机科学中的概率(算法分析、随机结构、相变等)[参见68W20, 68W40]

Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40]

68Q99

其它

None of the above, but in this section

68Rxx

同计算机科学有关的离散数学

Discrete mathematics in relation to computer science

68R01

一般理论

General

68R05

组合学

Combinatorics

68R10

图论(包括制图)[参见05Cxx, 90B10, 90B35, 90C35]

Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35]

68R15

字的组合学

Combinatorics on words

68R99

其它

None of the above, but in this section

68Txx

人工智能

Artificial intelligence

68T01

一般理论

General

68T05

学习和自适应系统[参见68Q32, 91E40]

Learning and adaptive systems [See also 68Q32, 91E40]

68T10

模式识别, 语音识别(聚类分析, 62H30)

Pattern recognition, speech recognition (For cluster analysis, see 62H30)

68T15

定理证明(推论、归结等)[参见03B35]

Theorem proving (deduction, resolution, etc.) [See also 03B35]

68T20

问题求解(启发式的、搜索策略等)

Problem solving (heuristics, search strategies, etc.)

68T27

人工智能中的逻辑

Logic in artificial intelligence

68T30

知识表示

Knowledge representation

68T35

语言和软件系统(基于知识系统、专家系统等)

Languages and software systems (knowledge-based systems, expert systems, etc.)

68T37

不确定性推理

Reasoning under uncertainty

68T40

机器人[参见93C85]

Robotics [See also 93C85]

68T42

代理技术

Agent technology

68T45

机器视觉和图像理解

Machine vision and scene understanding

68T50

自然语言处理[参见03B65]

Natural language processing [See also 03B65]

68T99

其它

None of the above, but in this section

68Uxx

计算方法论和应用

Computing methodologies and applications

68U01

一般理论

General

68U05

计算机制图; 计算几何[参见65D18]

Computer graphics; computational geometry [See also 65D18]

68U07

计算机辅助设计[参见65D17]

Computer-aided design [See also 65D17]

68U10

图象处理

Image processing

68U15

文本处理; 数学排印

Text processing; mathematical typography

68U20

模拟[参见65Cxx]

Simulation [See also 65Cxx]

68U35

信息系统(超文本导航、接口、决策支持等)[参见68M11]

Information systems (hypertext navigation, interfaces, decision support, etc.) [See also 68M11]

68U99

其它

None of the above, but in this section

68Wxx

算法(数值算法, 65-XX; 组合论和图论, 05C85, 68Rxx)

Algorithms (For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx)

68W01

一般理论

General

68W05

非数值算法

Nonnumerical algorithms

68W10

并行算法

Parallel algorithms

68W15

分布算法

Distributed algorithms

68W20

随机化算法

Randomized algorithms

68W25

近似算法

Approximation algorithms

68W27

在线算法

Online algorithms

68W30

符号计算和代数计算[参见11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]

Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]

68W32

串算法

Algorithms on strings

68W35

超大规模集成电路算法

VLSI algorithms

68W40

算法分析[参见68Q25]

Analysis of algorithms [See also 68Q25]

68W99

其它

None of the above, but in this section

70-XX

质点和系统力学(相对论力学, 83A05, 83C10; 统计力学, 82-XX)

Mechanics of particles and systems (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX)

70-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

70-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

70-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

70-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

70-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

70-05

实验工作

Experimental work

70-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

70-08

计算方法

Computational methods

70Axx

公理系统, 基础

Axiomatics, foundations

70A05

公理系统, 基础

Axiomatics, foundations

70A99

其它

None of the above, but in this section

70Bxx

运动学[参见53A17]

Kinematics [See also 53A17]

70B05

质点运动学

Kinematics of a particle

70B10

刚体运动学

Kinematics of a rigid body

70B15

力学, 机器人[参见68T40, 70Q05, 93C85]

Mechanisms, robots [See also 68T40, 70Q05, 93C85]

70B99

其它

None of the above, but in this section

70Cxx

静力学

Statics

70C20

静力学

Statics

70C99

其它

None of the above, but in this section

70Exx

刚体动力学和多体系统动力学

Dynamics of a rigid body and of multibody systems

70E05

陀螺仪的运动

Motion of the gyroscope

70E15

刚体自由运动[参见70M20]

Free motion of a rigid body [See also 70M20]

70E17

具有定点的刚体运动

Motion of a rigid body with a fixed point

70E18

同固体界面接触的刚体运动[参见70F25]

Motion of a rigid body in contact with a solid surface [See also 70F25]

70E20

刚体动力学的摄动方法

Perturbation methods for rigid body dynamics

70E40

运动的可积情形

Integrable cases of motion

70E45

较高维上推广

Higher-dimensional generalizations

70E50

稳定性问题

Stability problems

70E55

多体系统动力学

Dynamics of multibody systems

70E60

机器人动力学和控制[参见68T40, 70Q05, 93C85]

Robot dynamics and control [See also 68T40, 70Q05, 93C85]

70E99

其它

None of the above, but in this section

70Fxx

质点系统动力学, 包括天体力学

Dynamics of a system of particles, including celestial mechanics

70F05

二体问题

Two-body problems

70F07

三体问题

Three-body problems

70F10

n-体问题

n-body problems

70F15

天体力学

Celestial mechanics

70F16

天体力学中的碰撞, 正则化

Collisions in celestial mechanics, regularization

70F17

逆问题

Inverse problems

70F20

完整系统

Holonomic systems

70F25

非完整系统

Nonholonomic systems

70F35

刚体或伪刚体的碰撞

Collision of rigid or pseudo-rigid bodies

70F40

摩擦问题

Problems with friction

70F45

无限质点系统

Infinite particle systems

70F99

其它

None of the above, but in this section

70Gxx

一般模型、途径和方法[参见37-XX]

General models, approaches, and methods [See also 37-XX]

70G10

广义坐标; 事件空间, 冲击能空间, 构形空间, 状态空间或相空间

Generalized coordinates; event, impulse-energy, configuration, state, or phase space

70G40

拓扑方法和微分拓扑方法

Topological and differential-topological methods

70G45

微分几何方法(张量、联络、辛的、Poisson、接触、Riemann、非完整等)[参见53Cxx, 53Dxx, 58Axx]

Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx]

70G55

代数几何方法

Algebraic geometry methods

70G60

动力系统方法

Dynamical systems methods

70G65

对称, Lie群和Lie代数方法

Symmetries, Lie-group and Lie-algebra methods

70G70

泛函分析方法

Functional-analytic methods

70G75

变分法

Variational methods

70G99

其它

None of the above, but in this section

70Hxx

HamiltonLagrange力学[参见37Jxx]

Hamiltonian and Lagrangian mechanics [See also 37Jxx]

70H03

Lagrange方程

Lagrange’s equations

70H05

Hamilton方程

Hamilton’s equations

70H06

完全可积系统和积分方法

Completely integrable systems and methods of integration

70H07

不可积系统

Nonintegrable systems

70H08

近可积Hamilton系统, KAM理论

Nearly integrable Hamiltonian systems, KAM theory

70H09

扰动理论

Perturbation theories

70H11

绝热不变量

Adiabatic invariants

70H12

周期解和概周期解

Periodic and almost periodic solutions

70H14

稳定性问题

Stability problems

70H15

标准变换和辛变换

Canonical and symplectic transformations

70H20

Hamilton-Jacobi方程

Hamilton-Jacobi equations

70H25

Hamilton原理

Hamilton’s principle

70H30

其它变分原理

Other variational principles

70H33

对称律, 守恒律, 逆对称, 不变流形及其分歧, 约化

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction

70H40

相对论动力学

Relativistic dynamics

70H45

约束动力学, Dirac约束理论[参见70F20, 70F25, 70Gxx]

Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx]

70H50

更高阶理论

Higher-order theories

70H99

其它

None of the above, but in this section

70Jxx

线性振动理论

Linear vibration theory

70J10

模态分析

Modal analysis

70J25

稳定性

Stability

70J30

自由运动

Free motions

70J35

受迫运动

Forced motions

70J40

参量共振

Parametric resonances

70J50

结构振动问题的离散化系统

Systems arising from the discretization of structural vibration problems

70J99

其它

None of the above, but in this section

70Kxx

非线性动力学[参见34Cxx, 37-XX]

Nonlinear dynamics [See also 34Cxx, 37-XX]

70K05

相位平面分析, 极限环

Phase plane analysis, limit cycles

70K20

稳定性

Stability

70K25

自由运动

Free motions

70K28

参量共振

Parametric resonances

70K30

非线性共振

Nonlinear resonances

70K40

受迫运动

Forced motions

70K42

平衡轨道和周期轨道

Equilibria and periodic trajectories

70K43

拟周期运动和不变环面

Quasi-periodic motions and invariant tori

70K44

同宿轨道和异宿轨道

Homoclinic and heteroclinic trajectories

70K45

标准型

Normal forms

70K50

分叉和不稳定性

Bifurcations and instability

70K55

随机性转移(混沌性态)[参见37D45]

Transition to stochasticity (chaotic behavior) [See also 37D45]

70K60

一般扰动格式

General perturbation schemes

70K65

扰动平均

Averaging of perturbations

70K70

慢速和快速运动系统

Systems with slow and fast motions

70K75

非线性模式

Nonlinear modes

70K99

其它

None of the above, but in this section

70Lxx

随机振动[参见74H50]

Random vibrations [See also 74H50]

70L05

随机振动[参见74H50]

Random vibrations [See also 74H50]

70L99

其它

None of the above, but in this section

70Mxx

轨道力学

Orbital mechanics

70M20

轨道力学

Orbital mechanics

70M99

其它

None of the above, but in this section

70Pxx

可变质量, 火箭

Variable mass, rockets

70P05

可变质量, 火箭

Variable mass, rockets

70P99

其它

None of the above, but in this section

70Qxx

力学系统的控制[参见60Gxx, 60Jxx]

Control of mechanical systems [See also 60Gxx, 60Jxx]

70Q05

力学系统的控制[参见60Gxx, 60Jxx]

Control of mechanical systems [See also 60Gxx, 60Jxx]

70Q99

其它

None of the above, but in this section

70Sxx

经典场论[参见37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]

Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]

70S05

Lagrange形式体系, Hamilton形式体系

Lagrangian formalism and Hamiltonian formalism

70S10

对称律和守恒律

Symmetries and conservation laws

70S15

Yang-Mills和其它规范理论

Yang-Mills and other gauge theories

70S20

更一般非量子场论

More general nonquantum field theories

70S99

其它

None of the above, but in this section

74-XX

变形固体力学

Mechanics of deformable solids

74-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

74-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

74-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

74-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

74-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

74-05

实验工作

Experimental work

74-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

74Axx

连续固体力学的概论, 公理系统, 基础

Generalities, axiomatics, foundations of continuum mechanics of solids

74A05

变形运动学

Kinematics of deformation

74A10

应力

Stress

74A15

热力学

Thermodynamics

74A20

本构函数理论

Theory of constitutive functions

74A25

分子理论, 统计理论和动力学理论

Molecular, statistical, and kinetic theories

74A30

非单纯材料

Nonsimple materials

74A35

极性材料

Polar materials

74A40

随机材料和合成材料

Random materials and composite materials

74A45

破裂和破坏理论

Theories of fracture and damage

74A50

结构表面, 结构界面, 共存相

Structured surfaces and interfaces, coexistent phases

74A55

摩擦理论

Theories of friction (tribology)

74A60

微观力学理论

Micromechanical theories

74A65

反应材料

Reactive materials

74A99

其它

None of the above, but in this section

74Bxx

弹性材料

Elastic materials

74B05

经典线性弹性学

Classical linear elasticity

74B10

有初始应力的线性弹性学

Linear elasticity with initial stresses

74B15

形变状态(小形变迭加在大形变上)线性化方程

Equations linearized about a deformed state (small deformations superposed on large)

74B20

非线性弹性学

Nonlinear elasticity

74B99

其它

None of the above, but in this section

74Cxx

可塑性材料, 应力速率和内部可变型材料

Plastic materials, materials of stress-rate and internal-variable type

74C05

小应变, 速率无关理论(包括刚塑性和弹塑性材料)

Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)

74C10

小应变, 速率相关理论(包括粘塑性理论)

Small-strain, rate-dependent theories (including theories of viscoplasticity)

74C15

大应变, 速率无关理论(包括非线性塑性力学)

Large-strain, rate-independent theories (including nonlinear plasticity)

74C20

大应变, 速率相关理论

Large-strain, rate-dependent theories

74C99

其它

None of the above, but in this section

74Dxx

应变速率型材料和历史型材料, 其它具有记忆的材料(包括粘性阻尼弹性材料, 各种粘弹性材料)

Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)

74D05

线性本构方程

Linear constitutive equations

74D10

非线性本构方程

Nonlinear constitutive equations

74D99

其它

None of the above, but in this section

74Exx

特殊处理的材料性质

Material properties given special treatment

74E05

非均匀材料

Inhomogeneity

74E10

各向异性

Anisotropy

74E15

晶状结构

Crystalline structure

74E20

粒度

Granularity

74E25

织构

Texture

74E30

合成和混合性质

Composite and mixture properties

74E35

随机结构

Random structure

74E40

化学结构

Chemical structure

74E99

其它

None of the above, but in this section

74Fxx

固体力学与其它效应的耦合

Coupling of solid mechanics with other effects

74F05

热效应

Thermal effects

74F10

流体-固体相互作用(包括气动力弹性和流体弹性、多孔性等)

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

74F15

电磁效应

Electromagnetic effects

74F20

混合效应

Mixture effects

74F25

化学和活性效应

Chemical and reactive effects

74F99

其它

None of the above, but in this section

74Gxx

平衡(稳态)问题

Equilibrium (steady-state) problems

74G05

显式解

Explicit solutions

74G10

解的解析逼近(摄动法、渐近线法、级数等)

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)

74G15

解的数值逼近

Numerical approximation of solutions

74G20

解的局部存在性(接近一给定解)

Local existence of solutions (near a given solution)

74G25

解的整体存在性

Global existence of solutions

74G30

解的唯一性

Uniqueness of solutions

74G35

解的重数

Multiplicity of solutions

74G40

解的正则性

Regularity of solutions

74G45

解的界

Bounds for solutions

74G50

Saint-Venant原理

Saint-Venant’s principle

74G55

解的定性性态

Qualitative behavior of solutions

74G60

分叉和屈曲

Bifurcation and buckling

74G65

能量极小化

Energy minimization

74G70

应力集中, 奇异性

Stress concentrations, singularities

74G75

逆问题

Inverse problems

74G99

其它

None of the above, but in this section

74Hxx

动力学问题

Dynamical problems

74H05

显式解

Explicit solutions

74H10

解的解析逼近(扰动法、渐近线法、级数等)

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)

74H15

解的数值逼近

Numerical approximation of solutions

74H20

解的存在性

Existence of solutions

74H25

解的唯一性

Uniqueness of solutions

74H30

解的正则性

Regularity of solutions

74H35

奇异性, 爆破, 应力集中

Singularities, blowup, stress concentrations

74H40

解的长时间性态

Long-time behavior of solutions

74H45

振荡

Vibrations

74H50

随机振荡

Random vibrations

74H55

稳定性

Stability

74H60

动力学分歧

Dynamical bifurcation

74H65

混沌性态

Chaotic behavior

74H99

其它

None of the above, but in this section

74Jxx

Waves

74J05

线性波

Linear waves

74J10

体波

Bulk waves

74J15

表面波

Surface waves

74J20

波散射

Wave scattering

74J25

逆问题

Inverse problems

74J30

非线性波

Nonlinear waves

74J35

孤波

Solitary waves

74J40

激波和相关不连续性

Shocks and related discontinuities

74J99

其它

None of the above, but in this section

74Kxx

薄体, 结构

Thin bodies, structures

74K05

Strings

74K10

连杆(梁、柱、轴、拱、环等)

Rods (beams, columns, shafts, arches, rings, etc.)

74K15

薄膜

Membranes

74K20

Plates

74K25

壳体

Shells

74K30

接合

Junctions

74K35

薄膜

Thin films

74K99

其它

None of the above, but in this section

74Lxx

固体力学的特殊子域

Special subfields of solid mechanics

74L05

地球物理固体力学[参见86-XX]

Geophysical solid mechanics [See also 86-XX]

74L10

土力学和岩石力学

Soil and rock mechanics

74L15

生物固体力学[参见92C10]

Biomechanical solid mechanics [See also 92C10]

74L99

其它

None of the above, but in this section

74Mxx

问题的特殊类型

Special kinds of problems

74M05

控制, 开关和设备(“智能材料”)[参见93Cxx]

Control, switches and devices (“smart materials”) [See also 93Cxx]

74M10

摩擦

Friction

74M15

接触

Contact

74M20

冲击

Impact

74M25

微观力学

Micromechanics

74M99

其它

None of the above, but in this section

74Nxx

固体中的相变[参见74A50, 80Axx, 82B26, 82C26]

Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]

74N05

晶体

Crystals

74N10

位移变换

Displacive transformations

74N15

微观结构分析

Analysis of microstructure

74N20

相边界动力学

Dynamics of phase boundaries

74N25

扩散的变换

Transformations involving diffusion

74N30

滞后的问题

Problems involving hysteresis

74N99

其它

None of the above, but in this section

74Pxx

最优化[参见49Qxx]

Optimization [See also 49Qxx]

74P05

一致或权最优化

Compliance or weight optimization

74P10

其它性质的最优化

Optimization of other properties

74P15

拓扑方法

Topological methods

74P20

几何方法

Geometrical methods

74P99

其它

None of the above, but in this section

74Qxx

均匀化, 有效特征的测定

Homogenization, determination of effective properties

74Q05

平衡(衡态)问题的均匀化

Homogenization in equilibrium problems

74Q10

动力学问题的均匀性和振动

Homogenization and oscillations in dynamical problems

74Q15

有效本构方程

Effective constitutive equations

74Q20

有效特征界

Bounds on effective properties

74Q99

其它

None of the above, but in this section

74Rxx

裂纹和损伤

Fracture and damage

74R05

脆性损伤

Brittle damage

74R10

脆性裂纹

Brittle fracture

74R15

高速裂纹

High-velocity fracture

74R20

内摩擦裂纹和损伤

Anelastic fracture and damage

74R99

其它

None of the above, but in this section

74Sxx

数值方法[参见65-XX, 74G15, 74H15]

Numerical methods [See also 65-XX, 74G15, 74H15]

74S05

有限元()

Finite element methods

74S10

有限体积()

Finite volume methods

74S15

边界元()

Boundary element methods

74S20

有限差分()

Finite difference methods

74S25

()法和相关方法

Spectral and related methods

74S30

其它数值()

Other numerical methods

74S60

随机方法

Stochastic methods

74S70

复变量()

Complex variable methods

74S99

其它

None of the above, but in this section

76-XX

流体力学(一般连续力学, 74Axx74-XX其它部分)

Fluid mechanics (For general continuum mechanics, see 74Axx, or other parts of 74-XX)

76-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

76-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

76-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

76-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

76-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

76-05

实验工作

Experimental work

76-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

76Axx

基础, 结构方程, 流变学

Foundations, constitutive equations, rheology

76A02

流体力学基础

Foundations of fluid mechanics

76A05

Newton流体

Non-Newtonian fluids

76A10

粘弹性流体

Viscoelastic fluids

76A15

液晶[参见82D30]

Liquid crystals [See also 82D30]

76A20

流体薄膜

Thin fluid films

76A25

超流体(经典方面)

Superfluids (classical aspects)

76A99

其它

None of the above, but in this section

76Bxx

不可压缩非粘滞性流体

Incompressible inviscid fluids

76B03

存在性, 唯一性和正则性理论[参见35Q35]

Existence, uniqueness, and regularity theory [See also 35Q35]

76B07

自由界面位势流

Free-surface potential flows

76B10

射流和空腔, 空化, 自由流线理论, -入口问题, 机翼和水翼理论, 冲激

Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing

76B15

水波, 重力波; 弥散和散射, 非线性相互作用[参见35Q30]

Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]

76B20

船波

Ship waves

76B25

孤波[参见35C11]

Solitary waves [See also 35C11]

76B45

毛细现象(表面张力)[参见76D45]

Capillarity (surface tension) [See also 76D45]

76B47

涡流

Vortex flows

76B55

内部波

Internal waves

76B60

大气波[参见86A10]

Atmospheric waves [See also 86A10]

76B65

Rossby[参见86A05, 86A10]

Rossby waves [See also 86A05, 86A10]

76B70

非粘滞性流体中的层次效应

Stratification effects in inviscid fluids

76B75

流量控制和最优化[参见49Q10, 93C20, 93C95]

Flow control and optimization [See also 49Q10, 93C20, 93C95]

76B99

其它

None of the above, but in this section

76Dxx

不可压缩粘滞流体

Incompressible viscous fluids

76D03

存在性, 唯一性和正则性理论[参见35Q30]

Existence, uniqueness, and regularity theory [See also 35Q30]

76D05

Navier-Stokes方程

Navier-Stokes equations [See also 35Q30]

76D06

Navier-Stokes和相关方程的统计解[参见60H30, 76M35]

Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35]

76D07

Stokes流和相关(Oseen)

Stokes and related (Oseen, etc.) flows

76D08

润滑理论

Lubrication theory

76D09

()-非粘()性相互作用

Viscous-inviscid interaction

76D10

边界层理论, 分离和再附着, 高阶效应

Boundary-layer theory, separation and reattachment, higher-order effects

76D17

()性涡流

Viscous vortex flows

76D25

尾流和射流

Wakes and jets

76D27

其它自由-边界流; Hele-Shaw

Other free-boundary flows; Hele-Shaw flows

76D33

Waves

76D45

毛细现象(表面张力)[参见76B45]

Capillarity (surface tension) [See also 76B45]

76D50

()性流中的层次效应

Stratification effects in viscous fluids

76D55

流量控制和最优化[参见49Q10, 93C20, 93C95]

Flow control and optimization [See also 49Q10, 93C20, 93C95]

76D99

其它

None of the above, but in this section

76Exx

流体动力学的稳定性

Hydrodynamic stability

76E05

平行剪切流

Parallel shear flows

76E06

对流

Convection

76E07

旋转

Rotation

76E09

不平行流的稳定性和不稳定性

Stability and instability of nonparallel flows

76E15

绝对和对流的不稳定性和稳定性

Absolute and convective instability and stability

76E17

界面稳定性和不稳定性

Interfacial stability and instability

76E19

()压缩性效应

Compressibility effects

76E20

地球物理学和天体物理学流的稳定性和不稳定性

Stability and instability of geophysical and astrophysical flows

76E25

磁流体动力和电流体动力流的稳定性的不稳定性

Stability and instability of magnetohydrodynamic and electrohydrodynamic flows

76E30

非线性效应

Nonlinear effects

76E99

其它

None of the above, but in this section

76Fxx

湍流[参见37-XX, 60Gxx, 60Jxx]

Turbulence [See also 37-XX, 60Gxx, 60Jxx]

76F02

基础

Fundamentals

76F05

各向同性湍流; 齐次湍流

Isotropic turbulence; homogeneous turbulence

76F06

向湍流的转换

Transition to turbulence

76F10

剪切流

Shear flows

76F20

湍流的动力学系统方法[参见37-XX]

Dynamical systems approach to turbulence [See also 37-XX]

76F25

湍流输运, 混合

Turbulent transport, mixing

76F30

重正规化和其它场论方法[参见81T99]

Renormalization and other field-theoretical methods [See also 81T99]

76F35

对流湍流[参见76E15, 76Rxx]

Convective turbulence [See also 76E15, 76Rxx]

76F40

湍流边界层

Turbulent boundary layers

76F45

层次效应

Stratification effects

76F50

()压缩性效应

Compressibility effects

76F55

统计湍流建模 [参见76M35]

Statistical turbulence modeling [See also 76M35]

76F60

k-ε

k-ε modeling

76F65

湍流直接数值模拟和大涡流模拟

Direct numerical and large eddy simulation of turbulence

76F70

湍流控制

Control of turbulent flows

76F99

其它

None of the above, but in this section

76Gxx

一般空气动力学和亚音速流

General aerodynamics and subsonic flows

76G25

一般空气动力学和亚音速流

General aerodynamics and subsonic flows

76G99

其它

None of the above, but in this section

76Hxx

跨音速流

Transonic flows

76H05

跨音速流

Transonic flows

76H99

其它

None of the above, but in this section

76Jxx

超音速流

Supersonic flows

76J20

超音速流

Supersonic flows

76J99

其它

None of the above, but in this section

76Kxx

高超音速流

Hypersonic flows

76K05

高超音速流

Hypersonic flows

76K99

其它

None of the above, but in this section

76Lxx

激波和爆炸波[参见35L67]

Shock waves and blast waves [See also 35L67]

76L05

激波和爆炸波[参见35L67]

Shock waves and blast waves [See also 35L67]

76L99

其它

None of the above, but in this section

76Mxx

流体力学的基本方法[参见65-XX]

Basic methods in fluid mechanics [See also 65-XX]

76M10

有限元法

Finite element methods

76M12

有限体积法

Finite volume methods

76M15

边界元法

Boundary element methods

76M20

有限差分法

Finite difference methods

76M22

谱方法

Spectral methods

76M23

涡流方法

Vortex methods

76M25

其它数值方法

Other numerical methods

76M27

目测算法

Visualization algorithms

76M28

粒子方法和晶格-气体法

Particle methods and lattice-gas methods

76M30

变分法

Variational methods

76M35

随机分析

Stochastic analysis

76M40

复变量法

Complex-variables methods

76M45

渐近方法, 奇摄动

Asymptotic methods, singular perturbations

76M50

均匀性

Homogenization

76M55

维数分析和相似性

Dimensional analysis and similarity

76M60

对称分析, Lie群和代数法

Symmetry analysis, Lie group and algebra methods

76M99

其它

None of the above, but in this section

76Nxx

可压缩流体和气体动力学, 一般问题

Compressible fluids and gas dynamics, general

76N10

存在性, 唯一性和正则性理论[参见35L60, 35L65, 35Q30]

Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]

76N15

气体动力学, 一般问题

Gas dynamics, general

76N17

()-非粘()性相互作用

Viscous-inviscid interaction

76N20

边界层理论

Boundary-layer theory

76N25

()控制和最优化

Flow control and optimization

76N99

其它

None of the above, but in this section

76Pxx

稀薄气流, Boltzmann方程[参见82B40, 82C40, 82D05]

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]

76P05

稀薄气流, Boltzmann方程[参见82B40, 82C40, 82D05]

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]

76P99

其它

None of the above, but in this section

76Qxx

水声学和大气声学

Hydro- and aero-acoustics

76Q05

水声学和大气声学

Hydro- and aero-acoustics

76Q99

其它

None of the above, but in this section

76Rxx

扩散和对流

Diffusion and convection

76R05

受迫对流

Forced convection

76R10

自由对流

Free convection

76R50

扩散[参见60J60]

Diffusion [See also 60J60]

76R99

其它

None of the above, but in this section

76Sxx

多孔介质中的流; 滤波; 渗流

Flows in porous media; filtration; seepage

76S05

多孔介质中的流; 滤波; 渗流

Flows in porous media; filtration; seepage

76S99

其它

None of the above, but in this section

76Txx

两相流和多相流

Two-phase and multiphase flows

76T10

-气两相流, 起泡流

Liquid-gas two-phase flows, bubbly flows

76T15

粉尘-气体两相流

Dusty-gas two-phase flows

76T20

悬浮物

Suspensions

76T25

粒状流[参见74C99, 74E20]

Granular flows [See also 74C99, 74E20]

76T30

三相或多相流

Three or more component flows

76T99

其它

None of the above, but in this section

76Uxx

旋转流体

Rotating fluids

76U05

旋转流体

Rotating fluids

76U99

其它

None of the above, but in this section

76Vxx

流中的反应效应[参见80A32]

Reaction effects in flows [See also 80A32]

76V05

流中的反应效应[参见80A32]

Reaction effects in flows [See also 80A32]

76V99

其它

None of the above, but in this section

76Wxx

磁流体动力学和电流体动力学

Magnetohydrodynamics and electrohydrodyna­mics

76W05

磁流体动力学和电流体动力学

Magnetohydrodynamics and electrohydrodynamics

76W99

其它

None of the above, but in this section

76Xxx

电磁场中的电离气流; 等离子流[参见82D10]

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]

76X05

电磁场中的电离气流; 等离子流[参见82D10]

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]

76X99

其它

None of the above, but in this section

76Yxx

量子流体动力学和相对论流体动力学[参见82D50, 83C55, 85A30]

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]

76Y05

量子流体动力学和相对论流体动力学[参见82D50, 83C55, 85A30]

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]

76Y99

其它

None of the above, but in this section

76Zxx

生物流体力学[参见74F10, 74L15, 92Cxx]

Biological fluid mechanics [See also 74F10, 74L15, 92Cxx]

76Z05

生理学流[参见92C35]

Physiological flows [See also 92C35]

76Z10

水和空气中的生物推力

Biopropulsion in water and in air

76Z99

其它

None of the above, but in this section

78-XX

光学, 电磁理论(量子光学, 81V80)

Optics, electromagnetic theory (For quantum optics, see 81V80)

78-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

78-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

78-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

78-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

78-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

78-05

实验工作

Experimental work

78-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

78Axx

一般理论

General

78A02

基础

Foundations

78A05

几何光学

Geometric optics

78A10

物理光学

Physical optics

78A15

电子光学

Electron optics

78A20

空间电波

Space charge waves

78A25

电磁理论, 一般理论

Electromagnetic theory, general

78A30

电磁静力学

Electro- and magnetostatics

78A35

带电粒子的运动

Motion of charged particles

78A37

离子阱

Ion traps

78A40

波和辐射

Waves and radiation

78A45

衍射, 散射[WKB方法, 参见34E20]

Diffraction, scattering [See also 34E20 for WKB methods]

78A46

逆散射问题

Inverse scattering problems

78A48

合成介质; 随机介质

Composite media; random media

78A50

天线, 波导

Antennas, wave-guides

78A55

技术应用

Technical applications

78A57

电化学

Electrochemistry

78A60

激光, 微波激射器, 光的双稳性, 非线性光学[参见81V80]

Lasers, masers, optical bistability, nonlinear optics [See also 81V80]

78A70

在生物学上的应用[参见91D30, 92C30]

Biological applications [See also 91D30, 92C30]

78A97

数学上直观推断光学和电磁理论(还必须在这节至少指定一个其它分类号)

Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)

78A99

其它

Miscellaneous topics

78Mxx

基本方法

Basic methods

78M05

矩方法

Method of moments

78M10

有限元法

Finite element methods

78M12

有限体积法, 有限积分法

Finite volume methods, finite integration techniques

78M15

边界元法

Boundary element methods

78M16

多极法

Multipole methods

78M20

有限差分法

Finite difference methods

78M22

谱方法

Spectral methods

78M25

其它数值方法

Other numerical methods

78M30

变分法

Variational methods

78M31

Monte Carlo方法

Monte Carlo methods

78M32

神经和启发式方法

Neural and heuristic methods

78M34

模型归约

Model reduction

78M35

渐近分析

Asymptotic analysis

78M40

均匀性

Homogenization

78M50

最优化

Optimization

78M99

其它

None of the above, but in this section

80-XX

经典热力学, 热传导(固体热力学, 74A15)

Classical thermodynamics, heat transfer (For thermodynamics of solids, see 74A15)

80-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

80-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

80-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

80-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

80-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

80-05

实验论文

Experimental work

80-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

80Axx

()力学和热传导

Thermodynamics and heat transfer

80A05

基础

Foundations

80A10

经典热()力学, 包括相对论

Classical thermodynamics, including relativistic

80A17

连续介质热()力学[参见74A15]

Thermodynamics of continua [See also 74A15]

80A20

热质量转移, 热流

Heat and mass transfer, heat flow

80A22

Stefan问题、相变等[参见74Nxx]

Stefan problems, phase changes, etc. [See also 74Nxx]

80A23

逆问题

Inverse problems

80A25

燃烧

Combustion

80A30

化学动力学[参见76V05, 92C45, 92E20]

Chemical kinetics [See also 76V05, 92C45, 92E20]

80A32

化学反应流[参见92C45, 92E20]

Chemically reacting flows [See also 92C45, 92E20]

80A50

化学(一般问题)[主要见92Exx]

Chemistry (general) [See mainly 92Exx]

80A99

其它

None of the above, but in this section

80Mxx

基本方法

Basic methods

80M10

有限元法

Finite element methods

80M12

有限体积法

Finite volume methods

80M15

边界元法

Boundary element methods

80M20

有限差分法

Finite difference methods

80M22

谱方法

Spectral methods

80M25

其它数值方法

Other numerical methods

80M30

变分法

Variational methods

80M31

Monte Carlo方法

Monte Carlo methods

80M35

渐近分析

Asymptotic analysis

80M40

均匀性

Homogenization

80M50

最优化

Optimization

80M99

其它

None of the above, but in this section

81-XX

量子理论

Quantum theory

81-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

81-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

81-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

81-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

81-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

81-05

实验论文

Experimental papers

81-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

81-08

计算方法

Computational methods

81Pxx

公理系统, 基础, 哲学

Axiomatics, foundations, philosophy

81P05

一般问题和哲学问题

General and philosophical

81P10

量子力学的逻辑基础; 量子逻辑[参见03G12, 06C15]

Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15]

81P13

语境性

Contextuality

81P15

量子测量理论

Quantum measurement theory

81P16

量子态空间, 运算和概率概念

Quantum state spaces, operational and probabilistic concepts

81P20

随机力学(包括随机电动力学)

Stochastic mechanics (including stochastic electrodynamics)

81P40

量子相干性, 纠缠, 量子相关

Quantum coherence, entanglement, quantum correlations

81P45

量子信息, 通讯, 网络[参见94A15, 94A17]

Quantum information, communication, networks [See also 94A15, 94A17]

81P50

量子态估计, 近似克隆

Quantum state estimation, approximate cloning

81P68

量子计算[参见68Q05, 68Q12]

Quantum computation [See also 68Q05, 68Q12]

81P70

量子编码(一般理论)

Quantum coding (general)

81P94

量子密码学[参见94A60]

Quantum cryptography [See also 94A60]

81P99

其它

None of the above, but in this section

81Qxx

量子理论中的一般数学课题和方法

General mathematical topics and methods in quantum theory

81Q05

Schrödinger, Dirac, Klein-Gordon和其它量子力学方程的闭合解和近似解

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81Q10

量子理论中的自伴算子理论, 包括谱分析

Selfadjoint operator theory in quantum theory, including spectral analysis

81Q12

量子理论中的非自伴算子理论

Non-selfadjoint operator theory in quantum theory

81Q15

算子和微分方程的微扰理论

Perturbation theories for operators and differential equations

81Q20

包括WKBMaslov方法的半经典技术

Semiclassical techniques including WKB and Maslov methods

81Q30

Feynman积分和Feynman; 代数拓扑和代数几何的应用[参见14D05, 32S40]

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40]

81Q35

特殊空间: 流形、分形、图等上的量子力学

Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.

81Q37

量子点、波导、ratchets

Quantum dots, waveguides, ratchets, etc.

81Q40

Bethe-Salpeter和其它积分方程

Bethe-Salpeter and other integral equations

81Q50

量子混沌[参见37Dxx]

Quantum chaos [See also 37Dxx]

81Q60

超对称性和量子力学

Supersymmetry and quantum mechanics

81Q65

alternative量子力学

Alternative quantum mechanics

81Q70

微分-几何()法、包括完全相、BerryHannay相等

Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.

81Q80

特殊量子系统, 比如: 可解系统

Special quantum systems, such as solvable systems

81Q93

量子控制

Quantum control

81Q99

其它

None of the above, but in this section

81Rxx

量子理论中的群和代数

Groups and algebras in quantum theory

81R05

由物理学诱导的有限维群和代数及其表示[参见20C35, 22E70]

Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]

81R10

由物理学诱导的无限维群和代数, 包括Virasoro, Kac-Moody, W-代数与其它流行代数及其表示[参见17B65, 17B67, 22E65, 22E67, 22E70]

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]

81R12

与可积系统的关系[参见17Bxx, 37J35]

Relations with integrable systems [See also 17Bxx, 37J35]

81R15

算子代数法[参见46Lxx, 81T05]

Operator algebra methods [See also 46Lxx, 81T05]

81R20

协变式波动方程

Covariant wave equations

81R25

旋量和扭子法[参见32L25]

Spinor and twistor methods [See also 32L25]

81R30

相干态[参见22E45]; 压缩态[参见81V80]

Coherent states [See also 22E45]; squeezed states [See also 81V80]

81R40

对称破缺

Symmetry breaking

81R50

量子群和相关代数法[参见16T20, 17B37]

Quantum groups and related algebraic methods [See also 16T20, 17B37]

81R60

非交换几何

Noncommutative geometry

81R99

其它

None of the above, but in this section

81Sxx

一般量子力学和量子化问题

General quantum mechanics and problems of quantization

81S05

正则量子化, 交换关系和统计学

Canonical quantization, commutation relations and statistics

81S10

几何和量子化, 辛方法[参见53D50]

Geometry and quantization, symplectic methods [See also 53D50]

81S20

随机量子化

Stochastic quantization

81S22

开放系统, 约化动力学, 主方程, 去相干[参见82C31]

Open systems, reduced dynamics, master equations, decoherence [See also 82C31]

81S25

量子随机微积分

Quantum stochastic calculus

81S30

包括Wigner分布等的相空间方法

Phase space methods including Wigner distributions, etc.

81S40

路径积分[参见58D30]

Path integrals [See also 58D30]

81S99

其它

None of the above, but in this section

81Txx

量子场论; 相关经典场论[参见70Sxx]

Quantum field theory; related classical field theories [See also 70Sxx]

81T05

公理化量子场论; 算子代数

Axiomatic quantum field theory; operator algebras

81T08

构造量子场论

Constructive quantum field theory

81T10

模型量子场论

Model quantum field theories

81T13

Yang-Mills和其它度规理论[参见53C07, 58E15]

Yang-Mills and other gauge theories [See also 53C07, 58E15]

81T15

重正规化摄动法

Perturbative methods of renormalization

81T16

重正规化非摄动法

Nonperturbative methods of renormalization

81T17

重正规化群方法

Renormalization group methods

81T18

Feynman图解

Feynman diagrams

81T20

弯曲空间上的量子场论

Quantum field theory on curved space backgrounds

81T25

格上的量子场论

Quantum field theory on lattices

81T27

连续统极限

Continuum limits

81T28

热量子场论[参见82B30]

Thermal quantum field theory [See also 82B30]

81T30

弦和超弦理论; 其它广义对象(例如: branes)[参见83E30]

String and superstring theories; other extended objects (e.g., branes) [See also 83E30]

81T40

二维场论、共形场论等

Two-dimensional field theories, conformal field theories, etc.

81T45

拓扑场论[参见57R56, 58Dxx]

Topological field theories [See also 57R56, 58Dxx]

81T50

异常

Anomalies

81T55

Casimir效应

Casimir effect

81T60

超对称场论

Supersymmetric field theories

81T70

场论中的量子化; 上同调方法[参见58D29]

Quantization in field theory; cohomological methods [See also 58D29]

81T75

非交换几何法[参见46L85, 46L87, 58B34]

Noncommutative geometry methods [See also 46L85, 46L87, 58B34]

81T80

模拟和数值建模

Simulation and numerical modeling

81T99

其它

None of the above, but in this section

81Uxx

散射理论[参见34A55, 34L25, 34L40, 35P25, 47A40]

Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40]

81U05

2-体位势散射理论[WKB()法参见34E20]

2-body potential scattering theory [See also 34E20 for WKB methods]

81U10

n-体位势散射理论

n-body potential scattering theory

81U15

精确和拟可解系统

Exactly and quasi-solvable systems

81U20

S-矩阵论等

S-matrix theory, etc.

81U30

色散理论, 色散关系

Dispersion theory, dispersion relations

81U35

无弹性和多通道散射

Inelastic and multichannel scattering

81U40

逆散射问题

Inverse scattering problems

81U99

其它

None of the above, but in this section

81Vxx

在特殊物理系统中的应用

Applications to specific physical systems

81V05

强相互作用, 包括量子色动力学

Strong interaction, including quantum chromodynamics

81V10

电磁相互作用; 量子电动力学

Electromagnetic interaction; quantum electrodynamics

81V15

弱相互作用

Weak interaction

81V17

引力相互作用[参见83Cxx83Exx]

Gravitational interaction [See also 83Cxx and 83Exx]

81V19

其它基本相互作用

Other fundamental interactions

81V22

统一理论

Unified theories

81V25

其它基本粒子理论

Other elementary particle theory

81V35

核物理

Nuclear physics

81V45

原子物理

Atomic physics

81V55

分子物理[参见92E10]

Molecular physics [See also 92E10]

81V65

量子点[参见82D20]

Quantum dots [See also 82D20]

81V70

多体理论; 量子Hall效应

Many-body theory; quantum Hall effect

81V80

量子光学

Quantum optics

81V99

其它

None of the above, but in this section

82-XX

统计力学, 物质结构

Statistical mechanics, structure of matter

82-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

82-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

82-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

82-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

82-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

82-05

实验论文

Experimental papers

82-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

82-08

计算方法

Computational methods

82Bxx

平衡统计力学

Equilibrium statistical mechanics

82B03

基础

Foundations

82B05

经典平衡统计力学(一般问题)

Classical equilibrium statistical mechanics (general)

82B10

量子平衡统计力学(一般问题)

Quantum equilibrium statistical mechanics (general)

82B20

晶格系统(IsingdimerPotts)和图上系统

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82B21

连续统模型(粒子系统等)

Continuum models (systems of particles, etc.)

82B23

精确可解模型; Bethe拟设

Exactly solvable models; Bethe ansatz

82B24

界面问题; 扩散限制聚集

Interface problems; diffusion-limited aggregation

82B26

相变(一般问题)

Phase transitions (general)

82B27

临界现象

Critical phenomena

82B28

重正规化群方法[参见81T17]

Renormalization group methods [See also 81T17]

82B30

统计热动力学[参见80-XX]

Statistical thermodynamics [See also 80-XX]

82B31

随机方法

Stochastic methods

82B35

不可逆热动力学, 包括Onsager-Machlup理论[参见92E20]

Irreversible thermodynamics, including Onsager-Machlup theory [See also 92E20]

82B40

气体动力理论

Kinetic theory of gases

82B41

随机游动、随机表面、晶格animals[参见60G50, 82C41]

Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

82B43

渗透[参见60K35]

Percolation [See also 60K35]

82B44

无序系统(随机Ising模型、随机Schrödinger算子等)

Disordered systems (random Ising models, random Schrödinger operators, etc.)

82B80

数值方法(Monte Carlo、级数重新求和等)[参见65-XX, 81T80]

Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]

82B99

其它

None of the above, but in this section

82Cxx

不定常统计力学(动力学和非平衡)

Time-dependent statistical mechanics (dynamic and nonequilibrium)

82C03

基础

Foundations

82C05

经典动力学和非平衡统计力学(一般问题)

Classical dynamic and nonequilibrium statistical mechanics (general)

82C10

量子动力学和非平衡统计力学(一般问题)

Quantum dynamics and nonequilibrium statistical mechanics (general)

82C20

动力晶格系统(动力学Ising)和图上系统

Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

82C21

动力连续统模型(粒子系统等)

Dynamic continuum models (systems of particles, etc.)

82C22

交互作用粒子系统[参见60K35]

Interacting particle systems [See also 60K35]

82C23

精确可解动力模型[参见37K60]

Exactly solvable dynamic models [See also 37K60]

82C24

界面问题; 扩散限制聚集

Interface problems; diffusion-limited aggregation

82C26

动力学和非平衡相变(一般问题)

Dynamic and nonequilibrium phase transitions (general)

82C27

动力学临界现象

Dynamic critical phenomena

82C28

动力学重正规化群方法[参见81T17]

Dynamic renormalization group methods [See also 81T17]

82C31

随机方法(Fokker-PlanckLan­gevin)[参见60H10]

Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]

82C32

神经网[参见68T05, 91E40, 92B20]

Neural nets [See also 68T05, 91E40, 92B20]

82C35

不可逆热动力学, 包括Onsager-Machlup理论

Irreversible thermodynamics, including Onsager-Machlup theory

82C40

气体动力理论

Kinetic theory of gases

82C41

随机游动、随机表面、晶格animals等的动力学[参见60G50]

Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

82C43

不定常渗透[参见60K35]

Time-dependent percolation [See also 60K35]

82C44

无序系统(随机Ising系统等)的动力学

Dynamics of disordered systems (random Ising systems, etc.)

82C70

输运过程

Transport processes

82C80

数值方法(Monte Carlo、级数重新求和等)

Numerical methods (Monte Carlo, series resummation, etc.)

82C99

其它

None of the above, but in this section

82Dxx

在特殊类型物理系统中的应用

Applications to specific types of physical systems

82D05

气体

Gases

82D10

等离子体

Plasmas

82D15

液体

Liquids

82D20

固体

Solids

82D25

晶体(结晶群理论, 20H15)

Crystals (For crystallographic group theory, see 20H15)

82D30

随机介质, 无序材料(包括液晶和自旋玻璃)

Random media, disordered materials (including liquid crystals and spin glasses)

82D35

金属

Metals

82D37

半导体

Semiconductors

82D40

磁性材料

Magnetic materials

82D45

铁电体

Ferroelectrics

82D50

超流体

Superfluids

82D55

超导体

Superconductors

82D60

聚合物

Polymers

82D75

核反应堆理论; 中子输运

Nuclear reactor theory; neutron transport

82D77

量子波导, 量子线[参见78A50]

Quantum wave guides, quantum wires [See also 78A50]

82D80

纳米结构和纳米粒子

Nanostructures and nanoparticles

82D99

其它

None of the above, but in this section

83-XX

相对论和引力理论

Relativity and gravitational theory

83-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

83-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

83-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

83-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

83-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

83-05

实验工作

Experimental work

83-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

83-08

计算方法

Computational methods

83Axx

狭义相对论

Special relativity

83A05

狭义相对论

Special relativity

83A99

其它

None of the above, but in this section

83Bxx

观测问题和实验问题

Observational and experimental questions

83B05

观测问题和实验问题

Observational and experimental questions

83B99

其它

None of the above, but in this section

83Cxx

广义相对论

General relativity

83C05

Einstein方程(一般结构, 正则形式, Cauchy问题)

Einstein’s equations (general structure, canonical formalism, Cauchy problems)

83C10

运动方程

Equations of motion

83C15

精确解

Exact solutions

83C20

解的种类; 代数特殊解, 对称度量

Classes of solutions; algebraically special solutions, metrics with symmetries

83C22

Einstein-Maxwell方程

Einstein-Maxwell equations

83C25

近似方法, 弱场

Approximation procedures, weak fields

83C27

晶格引力, Regge微积分与其它离散方法

Lattice gravity, Regge calculus and other discrete methods

83C30

渐近()(辐射、新函数、H-空间等)

Asymptotic procedures (radiation, news functions, H-spaces, etc.)

83C35

引力波

Gravitational waves

83C40

引力能量和守恒律; 运动群

Gravitational energy and conservation laws; groups of motions

83C45

引力场的量子化

Quantization of the gravitational field

83C47

量子场论方法[参见81T20]

Methods of quantum field theory [See also 81T20]

83C50

电磁场

Electromagnetic fields

83C55

引力场同物质(流体动力学等)的宏观相互作用

Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)

83C57

黑洞

Black holes

83C60

旋量和扭子法; Newman-Penrose形式

Spinor and twistor methods; Newman-Penrose formalism

83C65

非交换几何方法[参见58B34]

Methods of noncommutative geometry [See also 58B34]

83C75

时空奇异性、宇宙的督察等

Space-time singularities, cosmic censorship, etc.

83C80

低维中的模拟

Analogues in lower dimensions

83C99

其它

None of the above, but in this section

83Dxx

Einstein相对引力理论, 包括非对称场论

Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

83D05

Einstein相对引力理论, 包括非对称场论

Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

83D99

其它

None of the above, but in this section

83Exx

统一场论, 高维场论和超场论

Unified, higher-dimensional and super field theories

83E05

几何动力学

Geometrodynamics

83E15

Kaluza-Klein和其它高维理论

Kaluza-Klein and other higher-dimensional theories

83E30

弦和超弦理论[参见81T30]

String and superstring theories [See also 81T30]

83E50

超引力

Supergravity

83E99

其它

None of the above, but in this section

83Fxx

宇宙论

Cosmology

83F05

宇宙论

Cosmology

83F99

其它

None of the above, but in this section

85-XX

天文学和天体物理学(天体力学, 70F15)

Astronomy and astrophysics (For celestial mechanics, see 70F15)

85-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

85-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

85-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

85-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

85-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

85-05

实验工作

Experimental work

85-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

85-08

计算方法

Computational methods

85Axx

天文学和天体物理学(天体力学, 70F15)

Astronomy and astrophysics (For celestial mech­anics, see 70F15)

85A04

一般问题

General

85A05

银河系和天体动力学

Galactic and stellar dynamics

85A15

银河系和天体结构

Galactic and stellar structure

85A20

行星大气

Planetary atmospheres

85A25

辐射传导

Radiative transfer

85A30

流体动力问题和流体磁力问题[参见76Y05]

Hydrodynamic and hydromagnetic problems [See also 76Y05]

85A35

统计天文学

Statistical astronomy

85A40

宇宙学(相对论的宇宙学, 83F05)

Cosmology (For relativistic cosmology, see 83F05)

85A99

各种课题

Miscellaneous topics

86-XX

地球物理学[参见76U05, 76V05]

Geophysics [See also 76U05, 76V05]

86-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

86-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

86-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

86-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

86-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

86-05

实验工作

Experimental work

86-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

86-08

计算方法

Computational methods

86Axx

地球物理学[参见76U05, 76V05]

Geophysics [See also 76U05, 76V05]

86A04

一般问题

General

86A05

水文学, 水文地理学, 海洋学[参见76Bxx, 76E20, 76Q05, 76Rxx, 76U05]

Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]

86A10

气象学和大气物理学[参见76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]

Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]

86A15

地震学

Seismology

86A17

地球动力学, 地震问题

Global dynamics, earthquake problems

86A20

位势, 勘探

Potentials, prospecting

86A22

逆问题[参见35R30]

Inverse problems [See also 35R30]

86A25

地电学和地磁学[参见76W05, 78A25]

Geo-electricity and geomagnetism [See also 76W05, 78A25]

86A30

大地测量学, 绘图问题

Geodesy, mapping problems

86A32

大地统计学

Geostatistics

86A40

冰川学

Glaciology

86A60

地质问题

Geological problems

86A99

各种课题

Miscellaneous topics

90-XX

运筹学, 数学规划

Operations research, mathematical pro­gramming

90-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

90-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

90-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

90-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

90-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

90-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

90-08

计算方法

Computational methods

90Bxx

运筹学和管理科学

Operations research and management science

90B05

库存, 存储, 储藏所

Inventory, storage, reservoirs

90B06

运输, 物流

Transportation, logistics

90B10

网络模型, 确定的

Network models, deterministic

90B15

网络模型, 随机的

Network models, stochastic

90B18

通信网络[参见68M10, 94A05]

Communication networks [See also 68M10, 94A05]

90B20

交通问题

Traffic problems

90B22

排队和服务[参见60K25, 68M20]

Queues and service [See also 60K25, 68M20]

90B25

可靠性, 有效性, 维修, 检查[参见60K10, 62N05]

Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

90B30

生产模型

Production models

90B35

调度理论, 确定的[参见68M20]

Scheduling theory, deterministic [See also 68M20]

90B36

调度理论, 随机的[参见68M20]

Scheduling theory, stochastic [See also 68M20]

90B40

搜索理论

Search theory

90B50

管理决策, 包括多目标[参见90C29, 90C31, 91A35, 91B06]

Management decision making, including multiple objectives [See also 90C29, 90C31, 91A35, 91B06]

90B60

市场营销, 广告[参见91B60]

Marketing, advertising [See also 91B60]

90B70

组织理论, 人力计划的理论[参见91D35]

Theory of organizations, manpower planning [See also 91D35]

90B80

分散选址和分配[参见90C10]

Discrete location and assignment [See also 90C10]

90B85

连续选址

Continuous location

90B90

面向案例研究

Case-oriented studies

90B99

其它

None of the above, but in this section

90Cxx

数学规划[参见49Mxx, 65Kxx]

Mathematical programming [See also 49Mxx, 65Kxx]

90C05

线性规划

Linear programming

90C06

大规模问题

Large-scale problems

90C08

线性规划的特殊问题(运输、多指标等)

Special problems of linear programming (transportation, multi-index, etc.)

90C09

Boole规划

Boolean programming

90C10

整数规划

Integer programming

90C11

混合整数规划

Mixed integer programming

90C15

随机规划

Stochastic programming

90C20

二次规划

Quadratic programming

90C22

半定规划

Semidefinite programming

90C25

凸规划

Convex programming

90C26

非凸规划, 全局最优化

Nonconvex programming, global optimization

90C27

组合最优化

Combinatorial optimization

90C29

多目标规划和目标规划

Multi-objective and goal programming

90C30

非线性规划

Nonlinear programming

90C31

灵敏度, 稳定性, 参量最优化

Sensitivity, stability, parametric optimization

90C32

分式规划

Fractional programming

90C33

互补性, 均衡问题和变分不等式(有限维)

Complementarity and equilibrium problems and variational inequalities (finite dimensions)

90C34

半无限规划

Semi-infinite programming

90C35

涉及图或网络的规划[参见90C27]

Programming involving graphs or networks [See also 90C27]

90C39

动态规划[参见49L20]

Dynamic programming [See also 49L20]

90C40

Markov和半Markov决策过程

Markov and semi-Markov decision processes

90C46

最优化条件, 对偶性[参见49N15]

Optimality conditions, duality [See also 49N15]

90C47

极小极大问题[参见49K35]

Minimax problems [See also 49K35]

90C48

抽象空间中的规划

Programming in abstract spaces

90C49

极值点和旋转方法

Extreme-point and pivoting methods

90C51

内点法

Interior-point methods

90C52

既约梯度型方法

Methods of reduced gradient type

90C53

Newton型方法

Methods of quasi-Newton type

90C55

逐次二次规划型方法

Methods of successive quadratic programming type

90C56

无导数法和使用广义导数的方法[参见49J52]

Derivative-free methods and methods using generalized derivatives [See also 49J52]

90C57

多面体组合学, 分枝定界, 分枝切割

Polyhedral combinatorics, branch-and-bound, branch-and-cut

90C59

近似法和启发式

Approximation methods and heuristics

90C60

数学规划问题的抽象计算复杂性[参见68Q25]

Abstract computational complexity for mathematical programming problems [See also 68Q25]

90C70

模糊规划

Fuzzy programming

90C90

数学规划的应用

Applications of mathematical programming

90C99

其它

None of the above, but in this section

91-XX

对策论, 经济学, 社会科学和行为科学

Game theory, economics, social and be­havioral sciences

91-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

91-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

91-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

91-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from section 01)

91-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

91-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

91-08

计算方法

Computational methods

91Axx

对策论

Game theory

91A05

2-人对策

2-person games

91A06

n-人对策, n >2

n-person games, n >2

91A10

非合作对策

Noncooperative games

91A12

合作对策

Cooperative games

91A13

无穷多局中人对策

Games with infinitely many players

91A15

随机对策

Stochastic games

91A18

扩展型对策

Games in extensive form

91A20

多级对策和重复对策

Multistage and repeated games

91A22

进化对策

Evolutionary games

91A23

微分对策[参见49N70]

Differential games [See also 49N70]

91A24

位置对策(追逃对策等)[参见49N75]

Positional games (pursuit and evasion, etc.) [See also 49N75]

91A25

动态对策

Dynamic games

91A26

推理, 学习

Rationality, learning

91A28

信号, 通信

Signaling, communication

91A30

对策的效用理论[参见91B16]

Utility theory for games [See also 91B16]

91A35

对策的决策理论[参见62Cxx, 91B06, 91B50]

Decision theory for games [See also 62Cxx, 91B06, 90B50]

91A40

对策论模型

Game-theoretic models

91A43

包括图的对策[参见05C57]

Games involving graphs [See also 05C57]

91A44

包括拓扑或集论的对策

Games involving topology or set theory

91A46

组合对策

Combinatorial games

91A50

离散时间对策

Discrete-time games

91A55

定时对策

Games of timing

91A60

概率对策; 赌博[参见60G40]

Probabilistic games; gambling [See also 60G40]

91A65

层次对策

Hierarchical games

91A70

对策空间

Spaces of games

91A80

对策论的应用

Applications of game theory

91A90

实验研究

Experimental studies

91A99

其它

None of the above, but in this section

91Bxx

数理经济学(计量经济学, 62P20)

Mathematical economics (For econometrics, see 62P20)

91B02

基础课题(基础数学, 方法论; 一般应用于经济)

Fundamental topics (basic mathematics, methodology; applicable to economics in general)

91B06

决策理论[参见62Cxx, 90B50, 91A35]

Decision theory [See also 62Cxx, 90B50, 91A35]

91B08

个体选择

Individual preferences

91B10

团体选择

Group preferences

91B12

表决理论

Voting theory

91B14

社会选择

Social choice

91B15

福利经济学

Welfare economics

91B16

效用理论

Utility theory

91B18

公共财产

Public goods

91B24

价格理论和市场结构

Price theory and market structure

91B25

资产定价模型

Asset pricing models

91B26

市场模型(拍卖、议价、出价、销售等)

Market models (auctions, bargaining, bidding, selling, etc.)

91B30

风险理论, 保险

Risk theory, insurance

91B32

资源和费用分配

Resource and cost allocation

91B38

生产理论, 企业理论

Production theory, theory of the firm

91B40

劳动市场, 合同

Labor market, contracts

91B42

消费行为, 需求理论

Consumer behavior, demand theory

91B44

信息经济学

Informational economics

91B50

一般均衡理论

General equilibrium theory

91B51

动态随机一般均衡理论

Dynamic stochastic general equilibrium theory

91B52

特殊均衡类型

Special types of equilibria

91B54

特殊经济类型

Special types of economies

91B55

经济动态学

Economic dynamics

91B60

贸易模型

Trade models

91B62

成长模型

Growth models

91B64

宏观经济模型(货币模型, 税收模型)

Macro-economic models (monetary models, models of taxation)

91B66

多部门模型

Multisectoral models

91B68

匹配模型

Matching models

91B69

异构主体模型

Heterogeneous agent models

91B70

随机模型

Stochastic models

91B72

空间模型

Spatial models

91B74

真实世界系统模型

Models of real-world systems

91B76

环境经济学(天然资源模型、收成、污染等)

Environmental economics (natural resource models, harvesting, pollution, etc.)

91B80

统计学和量子力学在经济学(经济物理学)的应用

Applications of statistical and quantum mechanics to economics (econophysics)

91B82

统计方法; 经济指标和经济度量

Statistical methods; economic indices and measures

91B84

经济时间序列分析[参见62M10]

Economic time series analysis [See also 62M10]

91B99

其它

None of the above, but in this section

91Cxx

社会科学和行为科学: 一般课题(统计学, 62-XX)

Social and behavioral sciences: general topics (For statistics, see 62-XX)

91C05

测量理论

Measurement theory

91C15

一维和多维定标

One- and multidimensional scaling

91C20

聚类[参见62H30]

Clustering [See also 62H30]

91C99

其它

None of the above, but in this section

91Dxx

数理社会学(包括人类学)

Mathematical sociology (including anthropology)

91D10

社会学, 社会和城市发展模型

Models of societies, social and urban evolution

91D20

数学地理学和数学人口统计学

Mathematical geography and demography

91D25

空间模型[参见91B72]

Spatial models [See also 91B72]

91D30

社会网络

Social networks

91D35

人力系统[参见91B40, 90B70]

Manpower systems [See also 91B40, 90B70]

91D99

其它

None of the above, but in this section

91Exx

数理心理学

Mathematical psychology

91E10

认识心理学

Cognitive psychology

91E30

心理物理学和心理生理学; 感觉

Psychophysics and psychophysiology; perception

91E40

记忆和学习[参见68T05]

Memory and learning [See also 68T05]

91E45

测量与性能

Measurement and performance

91E99

其它

None of the above, but in this section

91Fxx

其它社会科学和行为科学(数学处理)

Other social and behavioral sciences (mathematical treatment)

91F10

历史学, 政治学

History, political science

91F20

语言学[参见03B65, 68T50]

Linguistics [See also 03B65, 68T50]

91F99

其它

None of the above, but in this section

91Gxx

数理金融学

Mathematical finance

91G10

投资组合理论

Portfolio theory

91G20

衍生证券

Derivative securities

91G30

银行利率(随机模型)

Interest rates (stochastic models)

91G40

信贷风险

Credit risk

91G50

公司理财

Corporate finance

91G60

数值方法(包括Monte Carlo方法)

Numerical methods (including Monte Carlo methods)

91G70

统计方法, 计量经济学

Statistical methods, econometrics

91G80

其它理论的金融应用(随机控制, 变分法, 偏微分方程, 随机偏微分方程, 动力系统)

Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

91G99

其它

None of the above, but in this section

92-XX

生物学和其它自然科学

Biology and other natural sciences

92-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

92-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

92-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

92-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

92-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

92-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

92-08

计算方法

Computational methods

92Bxx

一般数学生物学

Mathematical biology in general

92B05

一般生物学和生物数学

General biology and biomathematics

92B10

分类学, 统计

Taxonomy, statistics

92B15

一般生物统计学[参见62P10]

General biostatistics [See also 62P10]

92B20

神经网络, 人工生命和相关课题[参见68T05, 82C32, 94Cxx]

Neural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx]

92B25

生物节律与同步现象

Biological rhythms and synchronization

92B99

其它

None of the above, but in this section

92Cxx

生理学, 细胞和医学课题

Physiological, cellular and medical topics

92C05

生物物理学

Biophysics

92C10

生物力学[参见74L15]

Biomechanics [See also 74L15]

92C15

发生生物学, 模式结构

Developmental biology, pattern formation

92C17

细胞运动(趋药性等)

Cell movement (chemotaxis, etc.)

92C20

神经生物学

Neural biology

92C30

生理学(一般问题)

Physiology (general)

92C35

生理学流[参见76Z05]

Physiological flow [See also 76Z05]

92C37

细胞生物学

Cell biology

92C40

生物化学, 分子生物学

Biochemistry, molecular biology

92C42

系统生物学, 网络

Systems biology, networks

92C45

生物化学问题中的动力学(药物动力学、酶动力学等)[参见80A30]

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]

92C50

药学应用(一般问题)

Medical applications (general)

92C55

生物医学图象和信号处理[参见44A12, 65R10]

Biomedical imaging and signal processing [See also 44A12, 65R10]

92C60

医学流行病学

Medical epidemiology

92C80

作物生物学

Plant biology

92C99

其它

None of the above, but in this section

92Dxx

遗传学和种群动力学

Genetics and population dynamics

92D10

遗传学(遗传代数, 17D92)

Genetics (For genetic algebras, see 17D92)

92D15

与进化有关的问题

Problems related to evolution

92D20

蛋白质序列, DNA序列

Protein sequences, DNA sequences

92D25

种群动力学(一般问题)

Population dynamics (general)

92D30

流行病学

Epidemiology

92D40

生态学

Ecology

92D50

动物行为

Animal behavior

92D99

其它

None of the above, but in this section

92Exx

化学(生物化学, 92C40)

Chemistry (For biochemistry, see 92C40)

92E10

分子结构(图论方法、微分拓扑方法等)

Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

92E20

经典流、经典反应等[参见80A30, 80A32]

Classical flows, reactions, etc. [See also 80A30, 80A32]

92E99

其它

None of the above, but in this section

92Fxx

其它自然科学(还必须在92-XX中至少指定一个分类号)

Other natural sciences (should also be assigned at least one other classification number in this section)

92F05

其它自然科学(还必须在92-XX中至少指定一个分类号)

Other natural sciences (should also be assigned at least one other classification number in section 92)

92F99

其它

None of the above, but in this section

93-XX

系统论; 控制(最优控制, 49-XX)

Systems theory; control (For optimal control, see 49-XX)

93-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

93-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

93-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

93-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

93-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

93-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

93Axx

一般理论

General

93A05

公理系统理论

Axiomatic system theory

93A10

一般系统

General systems

93A13

等级系统

Hierarchical systems

93A14

分散系统

Decentralized systems

93A15

大规模系统

Large scale systems

93A30

数学模型建立(系统模型、模型匹配等)

Mathematical modeling (models of systems, model-matching, etc.)

93A99

其它

None of the above, but in this section

93Bxx

可控性, 可观测性和系统结构

Controllability, observability, and system struc­ture

93B03

可达集

Attainable sets

93B05

可控性

Controllability

93B07

可观测性

Observability

93B10

标准结构

Canonical structure

93B11

系统结构简化

System structure simplification

93B12

变量结构系统

Variable structure systems

93B15

输入-输出数据的实现

Realizations from input-output data

93B17

变换

Transformations

93B18

线性化

Linearizations

93B20

极小系统表示

Minimal systems representations

93B25

代数方法

Algebraic methods

93B27

几何方法

Geometric methods

93B28

算子理论方法[参见47A48, 47A57, 47B35, 47N70]

Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]

93B30

系统辨识

System identification

93B35

灵敏度(鲁棒性)

Sensitivity (robustness)

93B36

H-控制

H-control

93B40

计算方法

Computational methods

93B50

综合问题

Synthesis problems

93B51

设计技术(鲁棒设计、计算机辅助设计等)

Design techniques (robust design, computer-aided design, etc.)

93B52

反馈控制

Feedback control

93B55

极点和零点配置问题

Pole and zero placement problems

93B60

特征值问题

Eigenvalue problems

93B99

其它

None of the above, but in this section

93Cxx

控制系统

Control systems

93C05

线性系统

Linear systems

93C10

非线性系统

Nonlinear systems

93C15

常微分方程控制系统[参见34H05]

Systems governed by ordinary differential equations [See also 34H05]

93C20

偏微分方程控制系统

Systems governed by partial differential equations

93C23

泛函-微分方程控制系统[参见34K35]

Systems governed by functional-differential equations [See also 34K35]

93C25

抽象空间中的系统

Systems in abstract spaces

93C30

函数关系而不是微分方程的控制系统(像混合与开关系统)

Systems governed by functional relations other than differential equations (such as hybrid and switching systems)

93C35

多变量系统

Multivariable systems

93C40

自适应控制

Adaptive control

93C41

不完全信息问题

Problems with incomplete information

93C42

模糊控制系统

Fuzzy control systems

93C55

离散时间系统

Discrete-time systems

93C57

抽样数据系统

Sampled-data systems

93C62

数字系统

Digital systems

93C65

离散事件系统

Discrete event systems

93C70

时标分析和奇异摄动

Time-scale analysis and singular perturbations

93C73

摄动

Perturbations

93C80

频率响应方法

Frequency-response methods

93C83

包括计算机的控制问题(过程控制等)

Control problems involving computers (process control, etc.)

93C85

自动系统(机器人等)[参见68T40, 70B15, 70Q05]

Automated systems (robots, etc.) [See also 68T40, 70B15, 70Q05]

93C95

应用

Applications

93C99

其它

None of the above, but in this section

93Dxx

稳定性

Stability

93D05

Lyapunov和其它经典稳定性(LagrangePoissonLplp)

Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)

93D09

鲁棒稳定性

Robust stability

93D10

反馈系统的Popov型稳定性

Popov-type stability of feedback systems

93D15

反馈系统的稳定化

Stabilization of systems by feedback

93D20

渐近稳定性

Asymptotic stability

93D21

自适应或鲁棒稳定化

Adaptive or robust stabilization

93D25

输入-输出方法

Input-output approaches

93D30

标量和向量Lyapunov函数

Scalar and vector Lyapunov functions

93D99

其它

None of the above, but in this section

93Exx

随机系统和控制

Stochastic systems and control

93E03

随机系统, 一般问题

Stochastic systems, general

93E10

估计和检测[参见60G35]

Estimation and detection [See also 60G35]

93E11

滤波[参见60G35]

Filtering [See also 60G35]

93E12

系统辨识

System identification

93E14

数据修匀

Data smoothing

93E15

随机稳定性

Stochastic stability

93E20

最优随机控制

Optimal stochastic control

93E24

最小二乘法和相关方法

Least squares and related methods

93E25

其它计算方法

Other computational methods

93E35

随机学习和自适应控制

Stochastic learning and adaptive control

93E99

其它

None of the above, but in this section

94-XX

信息和通讯, 电路

Information and communication, circuits

94-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

94-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

94-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

94-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

94-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

94-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

94Axx

通讯, 信息

Communication, information

94A05

通讯理论[参见60G35, 90B18]

Communication theory [See also 60G35, 90B18]

94A08

图象处理(压缩重构等)[参见68U10]

Image processing (compression, reconstruction, etc.) [See also 68U10]

94A11

正交和其它特殊函数的应用

Application of orthogonal and other special functions

94A12

信号理论(特征重构滤波等)

Signal theory (characterization, reconstruction, filtering, etc.)

94A13

检测理论

Detection theory

94A14

调幅和解调

Modulation and demodulation

94A15

信息理论, 一般问题[参见62B10, 81P94]

Information theory, general [See also 62B10, 81P94]

94A17

信息测度,

Measures of information, entropy

94A20

抽样理论

Sampling theory

94A24

编码定理(香农理论)

Coding theorems (Shannon theory)

94A29

源编码[参见68P30]

Source coding [See also 68P30]

94A34

速率畸变理论

Rate-distortion theory

94A40

信道模型(包括量子)

Channel models (including quantum)

94A45

前缀码, 长度可变码, 无逗号码[参见20M35, 68Q45]

Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]

94A50

调查表理论

Theory of questionnaires

94A55

移位寄存器序列和有限alphabets序列

Shift register sequences and sequences over finite alphabets

94A60

密码术[参见11T71, 14G50, 68P25, 81P94]

Cryptography [See also 11T71, 14G50, 68P25, 81P94]

94A62

鉴别和秘密共享[参见81P94]

Authentication and secret sharing [See also 81P94]

94A99

其它

None of the above, but in this section

94Bxx

误差校正码和误差检测码理论

Theory of error-correcting codes and error-detecting codes

94B05

线性码, 一般问题

Linear codes, general

94B10

卷积码

Convolutional codes

94B12

组合调幅方案(包括格子结构码)

Combined modulation schemes (including trellis codes)

94B15

循环码

Cyclic codes

94B20

段校正码

Burst-correcting codes

94B25

组合码

Combinatorial codes

94B27

几何方法(包括代数几何的应用)[参见11T71, 14G50]

Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]

94B30

主码

Majority codes

94B35

译码

Decoding

94B40

算术码[参见11T71, 14G50]

Arithmetic codes [See also 11T71, 14G50]

94B50

同步误差校正码

Synchronization error-correcting codes

94B60

其它类型码

Other types of codes

94B65

编码范围

Bounds on codes

94B70

误差概率

Error probability

94B75

凸集理论的应用和数的几何(覆盖半径等)[参见11H31]

Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H31]

94B99

其它

None of the above, but in this section

94Cxx

电路, 网络

Circuits, networks

94C05

解析电路理论

Analytic circuit theory

94C10

开关理论, Boole代数的应用; Boole函数[参见06E30]

Switching theory, application of Boolean algebra; Boolean functions [See also 06E30]

94C12

故障检测; 测试

Fault detection; testing

94C15

图论的应用[参见05Cxx, 68R10]

Applications of graph theory [See also 05Cxx, 68R10]

94C30

设计理论的应用[参见05Bxx]

Applications of design theory [See also 05Bxx]

94C99

其它

None of the above, but in this section

94Dxx

模糊集和模糊逻辑(94部分的问题有关)[参见03B52, 03E72, 28E10]

Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]

94D05

模糊集和模糊逻辑(94-XX的问题有关)[参见03B52, 03E72, 28E10]

Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]

94D99

其它

None of the above, but in this section

97-XX

数学教育

Mathematics education

97-00

一般参考书(手册、辞典、书目等)

General reference works (handbooks, dictionaries, bibliographies, etc.)

97-01

教学阐述(教科书、教学论文等)

Instructional exposition (textbooks, tutorial papers, etc.)

97-02

研究阐述(专著, 评述论文)

Research exposition (monographs, survey articles)

97-03

历史(还必须在01-XX中至少指定一个分类号)

Historical (must also be assigned at least one classification number from Section 01)

97-04

明显的机器计算和程序(非计算或程序设计理论)

Explicit machine computation and programs (not the theory of computation or programming)

97-06

会议录、会议、文集等

Proceedings, conferences, collections, etc.

97Axx

一般理论, 数学与教育

General, mathematics and education

97A10

综合作品, 参考书

Comprehensive works, reference books

97A20

娱乐数学, 游戏[参见00A08]

Recreational mathematics, games [See also 00A08]

97A30

数学与数学教育的历史[参见01-XX]

History of mathematics and mathematics education [See also 01-XX]

97A40

数学与社会

Mathematics and society

97A50

参考书目[参见01-00]

Bibliographies [See also 01-00]

97A70

论文与博士后论文

Theses and postdoctoral these

97A80

数学的普及

Popularization of mathematics

97A99

其它

None of the above, but in this section

97Bxx

教育政策和教育系统

Educational policy and educational systems

97B10

教育研究和教育计划

Educational research and planning

97B20

普通教育

General education

97B30

职业教育

Vocational education

97B40

高等教育

Higher education

97B50

教师进修(研究方面, 97C70)

Teacher education (For research aspects, see 97C70)

97B60

成人和继续教育

Adult and further education

97B70

教学大纲, 教育标准

Syllabuses, educational standards

97B99

其它

None of the above, but in this section

97Cxx

数学教育心理学和数学教育研究

Psychology of and research in mathematics education

97C10

综合作品

Comprehensive works

97C20

情感行为

Affective behavior

97C30

认知过程, 学习理论

Cognitive processes, learning theories

97C40

智力和才能

Intelligence and aptitudes

97C50

语言和口头交流

Language and verbal communication

97C60

学习的社会学方面

Sociological aspects of learning

97C70

教学过程

Teaching-learning processes

97C99

其它

None of the above, but in this section

97Dxx

数学教育和说明

Education and instruction in mathematics

97D10

综合作品, 比较研究

Comprehensive works, comparative studies

97D20

哲学和理论贡献(数学教学法)

Philosophical and theoretical contributions (maths didactics)

97D30

目标和目的

Objectives and goals

97D40

教学法和课堂技巧

Teaching methods and classroom techniques

97D50

教学问题的解决和启发式策略(研究方面, 97Cxx)

Teaching problem solving and heuristic strategies (For research aspects, see 97Cxx)

97D60

学生评估, 成绩控制和评定

Student assessment, achievement control and rating

97D70

学习难点和学生错误

Learning difficulties and student errors

97D80

教育机构和草拟课程

Teaching units and draft lessons

97D99

其它

None of the above, but in this section

97Exx

数学基础

Foundations of mathematics

97E10

综合作品

Comprehensive works

97E20

哲学和数学

Philosophy and mathematics

97E30

逻辑

Logic

97E40

数学语言

Language of mathematics

97E50

数学课堂上的推理与证明

Reasoning and proving in the mathematics classroom

97E60

集合, 关系, 集合论

Sets, relations, set theory

97E99

其它

None of the above, but in this section

97Fxx

算术, 数论

Arithmetic, number theory

97F10

综合作品

Comprehensive works

97F20

准数阶段, 数的概念

Pre-numerical stage, concept of numbers

97F30

自然数

Natural numbers

97F40

整数, 有理数

Integers, rational numbers

97F50

实数, 复数

Real numbers, complex numbers

97F60

数论

Number theory

97F70

测度与单位

Measures and units

97F80

比率和比例, 百分数

Ratio and proportion, percentages

97F90

现实生活中的数学, 实用算术

Real life mathematics, practical arithmetic

97F99

其它

None of the above, but in this section

97Gxx

几何

Geometry

97G10

综合作品

Comprehensive works

97G20

非形式几何

Informal geometry

97G30

面积和体积

Areas and volumes

97G40

平面和立体几何

Plane and solid geometry

97G50

变换几何

Transformation geometry

97G60

平面和球面三角学

Plane and spherical trigonometry

97G70

解析几何, 向量代数

Analytic geometry. Vector algebra

97G80

画法几何

Descriptive geometry

97G99

其它

None of the above, but in this section

97Hxx

代数

Algebra

97H10

综合作品

Comprehensive works

97H20

初级代数

Elementary algebra

97H30

方程和不等式

Equations and inequalities

97H40

, ,

Groups, rings, fields

97H50

有序代数结构

Ordered algebraic structures

97H60

线性代数

Linear algebra

97H99

其它

None of the above, but in this section

97Ixx

分析

Analysis

97I10

综合作品

Comprehensive works

97I20

映射和函数

Mappings and functions

97I30

序列和级数

Sequences and series

97I40

微分学

Differential calculus

97I50

积分学

Integral calculus

97I60

多变量函数

Functions of several variables

97I70

泛函方程

Functional equations

97I80

复分析

Complex analysis

97I99

其它

None of the above, but in this section

97Kxx

组合学, 图论, 概率论, 统计学

Combinatorics, graph theory, probability theo­ry, statistics

97K10

综合作品

Comprehensive works

97K20

组合学

Combinatorics

97K30

图论

Graph theory

97K40

描述统计学

Descriptive statistics

97K50

概率论

Probability theory

97K60

分布与随机过程

Distributions and stochastic processes

97K70

统计学的基础和方法论

Foundations and methodology of statistics

97K80

应用统计学

Applied statistics

97K99

其它

None of the above, but in this section

97Mxx

数学建模, 数学的应用

Mathematical modeling, applications of mathe­matics

97M10

建模与交叉学科

Modeling and interdisciplinarity

97M20

职业训练和职业教育中的数学

Mathematics in vocational training and career education

97M30

金融和保险数学

Financial and insurance mathematics

97M40

运筹学, 经济学

Operations research, economics

97M50

物理学, 天文学, 技术, 工程

Physics, astronomy, technology, engineering

97M60

生物学, 化学, 医学

Biology, chemistry, medicine

97M70

行为和社会科学

Behavioral and social sciences

97M80

艺术, 音乐, 语言, 建筑学

Arts, music, language, architecture

97M99

其它

None of the above, but in this section

97Nxx

数值数学

Numerical mathematics

97N10

综合作品

Comprehensive works

97N20

误差的舍入, 估计, 理论

Rounding, estimation, theory of errors

97N30

数值代数

Numerical algebra

97N40

数值分析

Numerical analysis

97N50

插值与逼近

Interpolation and approximation

97N60

数学规划

Mathematical programming

97N70

离散数学

Discrete mathematics

97N80

数学软件, 计算机程序

Mathematical software, computer programs

97N99

其它

None of the above, but in this section

97Pxx

计算机科学

Computer science

97P10

综合作品

Comprehensive works

97P20

计算机科学理论

Theory of computer science

97P30

系统软件

System software

97P40

程序设计语言

Programming languages

97P50

程序设计技术

Programming techniques

97P60

硬件

Hardware

97P70

计算机科学与社会

Computer science and society

97P99

其它

None of the above, but in this section

97Qxx

计算机科学教育

Computer science education

97Q10

综合作品

Comprehensive works

97Q20

计算机科学教学中的情感因素

Affective aspects in teaching computer science

97Q30

认知过程

Cognitive processes

97Q40

社会学方面

Sociological aspects

97Q50

目标

Objectives

97Q60

教学方法和课堂教学技巧

Teaching methods and classroom techniques

97Q70

学生评价

Student assessment

97Q80

教学单位

Teaching units

97Q99

其它

None of the above, but in this section

97Rxx

计算机科学应用

Computer science applications

97R10

综合作品, 程序集

Comprehensive works, collections of programs

97R20

在数学中的应用

Applications in mathematics

97R30

在科学中的应用

Applications in sciences

97R40

人工智能

Artificial intelligence

97R50

数据库, 信息系统

Data bases, information systems

97R60

计算机图形学

Computer graphics

97R70

用户程序, 管理应用

User programs, administrative applications

97R80

娱乐计算

Recreational computing

97R99

其它

None of the above, but in this section

97Uxx

教材和()媒体, 教育技术

Educational material and media, educational technology

97U10

综合作品

Comprehensive works

97U20

教科书.教科书研究

Textbooks. Textbook research

97U30

教师手册和计划辅助设备

Teachers’ manuals and planning aids

97U40

问题集.竞赛.考试

Problem books. Competitions. Examination

97U50

计算机辅助教学; e-学习

Computer assisted instruction; e-learning

97U60

操作材料

Manipulative materials

97U70

技术工具, 计算器

Technological tools, calculators

97U80

视听媒体

Audiovisual media

97U99

其它

None of the above, but in this section


146